used fuel degradation: experimental and modeling report · 2013. 12. 9. · developed an idealized...
TRANSCRIPT
Used Fuel Degradation: Experimental and Modeling Report
(FCRD-UFD-2013-000404)
Prepared for
U.S. Department of Energy
Used Fuel Disposition Campaign
David C. Sassani, Carlos F. Jové Colón, Philippe Weck
(Sandia National Laboratories)
James L. Jerden Jr., Kurt E. Frey, Terry Cruse, William L. Ebert (Argonne National Laboratory)
Edgar C. Buck, Richard S. Wittman
(Pacific Northwest National Laboratory)
October 17, 2013
SAND2013- 9077P
Prepared by:
Sandia National Laboratories
Albuquerque, New Mexico 87185
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia
Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of
Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
DISCLAIMER
This information was prepared as an account of work sponsored by an
agency of the U.S. Government. Neither the U.S. Government nor any
agency thereof, nor any of their employees, makes any warranty,
expressed or implied, or assumes any legal liability or responsibility for
the accuracy, completeness, or usefulness, of any information, apparatus,
product, or process disclosed, or represents that its use would not infringe
privately owned rights. References herein to any specific commercial
product, process, or service by trade name, trade mark, manufacturer, or
otherwise, does not necessarily constitute or imply its endorsement,
recommendation, or favoring by the U.S. Government or any agency
thereof. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the U.S. Government or any agency
thereof.
Used Fuel Degradation: Experimental and Modeling Report October 2013 iii
Used Fuel Degradation: Experimental and Modeling Report iv October 2013
AKNOWLEDGEMENTS
The authors acknowledge our gratitude to Yifeng Wang (SNL), Geoff Freeze (SNL), Peter Swift
(SNL), Kevin McMahon (SNL), William Spezialetti (DOE NE-53), Prasad Nair (DOE NE-53),
Mark Tynan (DOE NE-53), Joseph Price (DOE NE-53) and Tim Gunther (DOE NE-53) for their
helpful discussions on topics covered in this report.
Used Fuel Degradation: Experimental and Modeling Report October 2013 v
SUMMARY
The contributions presented in this report are being accomplished via a concerted effort among
three different national laboratories: SNL, ANL and PNNL. This collaborative approach to the
used fuel degradation and radionuclide mobilization (UFD&RM) activities includes
experimental work, process model development (including first-principles approaches) and
model integration—both internally among developed process models and between developed
process models and PA models. Figure S-1 depicts a summary schematic of the major models,
experimental studies, and their primary handoffs to each other, as well as the major outputs that
currently would feed performance assessment (PA) models as a result of the integrated
execution of this work.
The primary outputs of these cumulative UFD&RM activities provide two connections into the
PA models. The primary output connection is the fractional degradation rate (FDR) of the used
fuel matrix. Within the current PA models, this parameter is sampled from a distribution of
reported values in the literature, but may now be generated directly from these process-based
models (both the radiolysis model and the mixed potential model are used to evaluate this
result). In addition, a second output has been generated to represent the instant release fractions
(IRF) of radionuclides that are released virtually instantaneously upon breach of the cladding.
As indicated in Figure S-1, two sets of distributions are recommended, a set of uniform
distributions that are parameterized as a function of burnup and a set of triangular distributions
that have no functional dependencies. Both of these sets of IRF distributions capture
uncertainties in their parameterization. Sampling of these IRF distributions can be done
directly within the PA model at the initial time of UF degradation for each fuel rod represented
as having a breach in its cladding.
Within the process models, the radiolysis model (RM) and the mixed potential model (MPM)
may be used separately to evaluate (a) the generation rate of radiolytic oxidants in a water film
on the surface of a used fuel pellet, and (b) the degradation rate of used fuel at the pellet-water
film interface for a given generation rate of radiolytic oxidant, respectively. In addition, these
two model tools can be used to evaluate the degradation of used fuel of a given burnup under
post-closure conditions where decay and thermal evolution occur. These two models operate
on very different time scales. The RM evaluates multiple coupled reactions that occur in
miniscule fractions of a second and that reach steady state in minutes to hours. The MPM
generally evaluates timesteps of months to years to hundreds of years. The feedback between
these two models has been implemented by hand to this point, but progress has been made in
developing detailed coupling strategies for merging these two process models into a single
coupled module.
Underpinning these continuum modeling approaches are experimental studies and first
principles models of uranium dioxide and the major corrosion products expected. As well as
providing conceptual guidance to the modeling approaches, the experimental programs at both
ANL and PNNL have provided validation data for the conceptual models and parametric
constraints for improving the modeling tools. Detailed mechanistic processes have also been
investigated using first principles molecular scale modeling for UO2 and some of its common
corrosion products. Such work also provides methods for predicting thermochemical properties
where data are lacking, and can provide insight and validation for processes evaluated in
detailed electrochemical experiments where multiple mechanisms are all possible.
Used Fuel Degradation: Experimental and Modeling Report vi October 2013
Figure ES-1. Schematic diagram of the integration among activities for used fuel degradation and the connection to a performance
assessment model. Experimental work (triangles) and first principles models (diamond) shown as underpinning process models.
Used Fuel Degradation: Experimental and Modeling Report October 2013 vii
The main accomplishments of these activities are summarized as follows:
Developed an idealized strategy for integrating used fuel degradation process models
with PA models to analyze generic disposal environments. This strategy includes
parametric connections/couplings needed for direct incorporation into PA models
(Section 1.2.2). However, it is an ongoing task to delineate in the implementation
specifics of how these process models will couple to other EBS process submodels
within the PA model for generic disposal environment evaluations of a safety case.
Additional more simplified coupling options are outlined that have fewer open
constraints on implementation specifics and provide flexible options for incorporating
additional coupling detail as needed.
Delineated constraints for the instant release fractions (IRF –Section 1) from used
nuclear fuel. The constraints are implemented in two sets of distributions: (a) triangular
distributions representing minimum, maximum, and mean (apex) values for LWR UF
with BU at or below 50 MWd/KgU, and (b) uniform distributions as a function of BU
representing instantaneous radionuclide releases for UF with BU up to 75 MWd/KgU.
In future work, additional data may allow delineation of the accessible grain boundaries
(and pellet fractures) from inaccessible grain boundaries (and pellet fractures) to better
delineate constraints on the IRF. Currently, all grain boundaries (and pellet fractures)
are considered accessible.
Developed and implemented a radiolysis model (RM - Section 2) using a
comprehensive set of coupled radiolysis kinetic reactions to better account for potential
solution compositions to be encountered in repository environments (Wittman and
Buck, 2012). Radiolytic species are generated at a rate that is based on the dose rate
induced by the used fuel radiation field deposited in the water film on the fuel pellet.
The current model covers the H2O system and allows for dissolved carbonate by
considering heterogeneous CO2 (aq) speciation including HCO-3. Comparisons of
modeling results are in good agreement with those reported in other studies. The model
inputs are the reaction rate constants, the temperature and dose rate, the generation rates
of radiolytic species, and the initial concentrations of species in the system. In these
idealized systems, hydrogen peroxide is the primary oxidizing species generated in the
radiolytic process. The conditional generation rate for H2O2 production is the primary
output provided to the model for matrix degradation rate (i.e., the mixed potential
model).
Implemented and verified/validated the Canadian mixed potential model for UO2 fuel
corrosion in the initial mixed potential model (MPM - Jerden et al., 2013). The
objective of the MPM (Section 3) is to calculate the used fuel degradation rates for a
wide range of disposal environments to provide the source term radionuclide release
rates for generic repository concepts. The fuel degradation rate is calculated for
chemical and oxidative dissolution mechanisms using mixed potential theory to account
for all relevant redox reactions at the fuel surface, including those involving oxidants
produced by solution radiolysis. This MPM is based on the fundamental
electrochemical and thermodynamic properties described by interactions at the fuel –
fluid interface and captures key processes such as hydrogen oxidation and the catalysis
of oxidation/reduction reactions by noble metal (epsilon) particles on the fuel surface. If
Used Fuel Degradation: Experimental and Modeling Report viii October 2013
radiolytic oxidants are exhausted by reaction with hydrogen in the EBS (e.g., supplied
from corrosion processes), then the degradation rate becomes controlled by UO2
solubility constraints (chemical dissolution) and the degradation rate is affected directly
by the rate of transport of uranium away from the used fuel. If oxidative dissolution is
the dominant process, then the MPM directly calculates the rate of used fuel matrix
degradation. Jerden et al. (2013) provides an archived version of Rev 01 of the MPM.
Additional computational capability to address the role of epsilon particles in reducing
radiolytic oxidants is added to the current version (Section 7). The MPM was
developed to account for the following key phenomena (Jerden et al. 2013):
o Rate of oxidative dissolution of the fuel matrix as determined by interfacial redox
reaction kinetics (quantified as corrosion potential) occurring at the multiphase fuel
surface (phases include UO2 and the fission product alloy or epsilon phase).
o Chemical (or solubility-based) dissolution of the fuel matrix.
o Complexation of dissolved uranium by carbonate near the fuel surface and in the bulk
solution.
o Production of hydrogen peroxide (the dominant fuel oxidant in anoxic repository
environments) by alpha-radiolysis.
o Diffusion of reactants and products in the groundwater away from and towards the
reacting fuel surface.
o Precipitation and dissolution of a U–bearing corrosion product layer on the fuel
surface.
o Diffusion of reactants and products through the porous and tortuous corrosion layer
covering the reacting fuel surface.
o Arrhenius-type temperature dependence for all interfacial and bulk reactions.
Advanced strategies for coupling the RM and MPM into a single fuel matrix
degradation (FMD) module (Section 4) for use in analyzing the matrix degradation rate
(fractional and absolute) of used fuel. Parameters needed to couple the codes and four
strategies for implementing the coupling of the two process models are described in
detail (Section 4). Different options have advantages and disadvantages based on the
extent of coding that would be required and the ease of use of the final product. The
four approaches for implementing coupling are:
o Option 1: Add radiolysis model as subroutine within mixed potential model
code. This would involve re-coding the RM from Fortran into MATLAB or
alternatively recoding the MPM into Fortran so that the two models would run
as part of the same program.
Pros: full RM code included in integrated model, not limited to
abstracted form of the RM, seamless transfer of information.
Cons: relatively large amount of time and effort required to support
recoding.
o Option 2: Represent radiolysis model as an analytical expression within mixed
potential model code. This would involve minimal coding in MATLAB, but
would require significant effort to define an analytical form that captures the
full range of conditional dependencies accounted for in the RM.
Used Fuel Degradation: Experimental and Modeling Report October 2013 ix
Pros: coding work is streamlined and simplified, seamless transfer of
information.
Cons: uncertainty of success of approach, it is not clear that a single
analytical expression can capture all of the relevant conditional
dependencies accounted for in the full RM.
o Option 3: Provide radiolysis model results as look-up table of conditional
generation values produced by running the RM over the full range of relevant
conditions. This generation value look-up table would be treated by the MPM
as part of the parameter database.
Pros: little to no coding work needed, seamless transfer of information.
Cons: relatively large amount of time and effort to produce exhaustive
table that considers all relevant conditions,
o Option 4: Maintain radiolysis model and mixed potential model as separate
codes that call each other during a fuel degradation model run.
Pros: little to no coding work needed, not limited to abstracted version of
the RM.
Cons: uncertainty of success of approach, it is not clear that the Fortran
and MATLAB codes and pass the needed information back and forth as
they currently exist. Even if possible this approach may dramatically
increase computing time needed to run the FDM.
The last of these four options is closest to the approach to the sensitivity analyses for the
MPM implemented within DAKOTA presented in Section 4.3.1. However, integration of
the RM into this implementation has not been completed at this point and would require
either a dynamic link library to implement, or additional coding within the DAKOTA
environment to manage parameter hand-offs between the MPM and RM.
Completed computational first-principles studies of the structures of the uranyl
peroxide hydrates studtite and metastudtite (Weck et al., 2012) and of the bulk and
surface chemistry of UO2 (Weck et al., 2013). The structures of the uranyl peroxide
hydrates obtained from total energy calculations using density functional theory are in
very good agreement with those characterized by experimental X-ray diffraction
methods. Such work tests this computational tool to predict thermodynamic properties
of fuel corrosion products (e.g., uranyl peroxide hydrates) for used with similar studies
of UO2 bulk and surface chemistry (Weck et al., 2013).
Conclusions and future development
Our general strategy for integrating process models with each other, and within the
performance assessment models, is to identify initially the major feeds among the process
models (Section 4) and from the process models to performance assessment models (Section
1). For coupling into performance assessment models, our approach begins by using the
existing interface connections in the PA model and progresses to adding further connections as
the process models develop and become more highly coupled. The ultimate objective is to
support the PA models with a single coupled process model for analyzing the fractional
Used Fuel Degradation: Experimental and Modeling Report x October 2013
degradation rate of used fuel. Note that even after coupling, the radiolysis model (RM) and the
mixed potential model (MPM) can still be used individually for detailed sensitivity and
uncertainty analyses as well.
Currently, the MPM has been coupled with DAKOTA to perform parametric sensitivity analyses
for major input variables such as radiation flux, temperature, and chemical species variability.
The DAKOTA code provides one possible means of handshaking or coupling the MPM with the
RM. Within any coupling implementation, identifying the essential parameters to be exchanged
is the primary step. One of these is the conditional generation rate of hydrogen peroxide (Gcond)
as a function of energy deposition in the water film on the used fuel pellet surface. The value of
Gcond is calculated in the RM and handed off to the MPM. Within the MPM, the Gcond is used to
calculate the spatial generation of [H2O2] from the dose rate as affected by surface reactions with
the fuel and diffusive flux of the species.
The coupling of the RM and MPM is implemented currently by running the models separately
because the MPM uses time steps on the order of years, whereas the RM uses time steps on the
order of seconds. An alternative to actively linking the RM and MPM (perhaps within
DAKOTA) is to develop an analytic expression that determines Gcond for a given set of
conditions. The analytic expression could be coded directly into the MPM via the MATLAB
implementation, and thus run directly within the MPM. However, this simplification does not
establish a true working link and the full capabilities of RM would be lost without further work.
Furthermore, the determination of analytical expressions for the full ranges of environments may
prove to be onerous.
Currently the only radiolytic species in the MPM is H2O2. Other radiolytic species will need to
be added to the MPM for it to be applicable to the full range of relevant geologic and EBS
environments. The radiolytic species that need to be added can be determined by sensitivity runs
using the RM (which evaluates a more detailed set of compositional components) for the range
of relevant solution compositions for sites of interest. The focus of RM sensitivity runs is on
radiolytically active species (for example: Cl-, Br
-, NO3
-, CO3
2-, SO4
2-) and can be used to
determine concentration thresholds above which radiolytic species other than H2O2 significantly
impact fuel oxidation.
Density functional theory (DFT) calculations of the thermodynamic properties of crystalline
studtite, (UO2)O2(H2O)4, and metastudtite, (UO2)O2(H2O)2, were carried out within the generalized
gradient approximation to derive both their isochoric and isobaric thermal properties. Further
experimental work is needed to assess our theoretical predictions for these SNF corrosion phases.
This methodology will be applied in a systematic way to other possible metastable corrosion
phases and other NS and EBS models to expand the applicability of this data set to more realistic
systems. In addition, polymorphism in stoichiometric dehydrated schoepite, UO2(OH)2, was
investigated using computational approaches that go beyond standard DFT. The results show that
standard DFT is sufficient for this system. The three UO2(OH)2 phase structures optimized with
standard DFT will be used in future calculations of the thermodynamic stability and phase
transitions in this compound.
For the UFD&RM process models and/or coupled modules, the primary connection into the
performance assessment models is the fractional degradation rate (FDR) parameter, which is
currently sampled from a distribution. This primary connection has been the focus for developing
more process-based models that are able to supplant the FDR distribution by supplying that
Used Fuel Degradation: Experimental and Modeling Report October 2013 xi
parameter directly as a result of the process model. In addition, a second connection within the
PA model could be generated to represent the instant release fractions. Sampling of the IRF
distributions within the PA model would be done similar to the current sampling of the FDR
distribution and would describe the fast/instant release fraction radionuclides that are mobilized
instantly at the time of cladding breach. The distributions for the IRF would only need to be
sampled at the initiation of UF degradation for each fuel rod represented as having a breach in its
cladding.
Used Fuel Degradation: Experimental and Modeling Report xii October 2013
TABLE OF CONTENTS
Summary ...................................................................................................................................................... v
Acronyms and Abbreviations .................................................................................................................... xiii
1. MODEL OVERVIEW AND INTEGRATION ................................................................................. 1
1.1 Introduction .............................................................................................................................. 1 1.1.1 Coupling the Mixed Potential and Radiolysis Models for Used Fuel
Degradation ................................................................................................................. 1
1.2 Background and Overview of Models ..................................................................................... 2 1.2.1 Used Fuel degradation processes within the engineered barrier system ..................... 3 1.2.2 Used Fuel Degradation and Radionuclide Mobilization Concepts and
Models ......................................................................................................................... 6 1.2.3 Integration into the performance assessment models ................................................ 12 1.2.4 Summary ................................................................................................................... 18
2. SUMMARY OF RADIOLYSIS MODEL ....................................................................................... 19
2.1 Objective ................................................................................................................................ 19
2.2 Physical Model ....................................................................................................................... 19
2.3 Mathematical model ............................................................................................................... 21 2.3.1 Geometric scale ......................................................................................................... 22 2.3.2 Time scale ................................................................................................................. 23
3. SUMMARY OF MIXED POTENTIAL MODEL ........................................................................... 25
3.1 Objective and Background ..................................................................................................... 25
3.2 Physical model ....................................................................................................................... 26
3.3 Mathematical Model .............................................................................................................. 29 3.3.1 Geometric Scale ........................................................................................................ 30 3.3.2 Time Scale ................................................................................................................ 30
3.4 Example of MPM Calculations .............................................................................................. 30
4. COUPLING MPM/RM MODELS ................................................................................................... 33
4.1 Parameter values provided by RM to MPM........................................................................... 34
4.2 Parameter values provided by MPM to RM........................................................................... 34
4.3 Interface Approaches ............................................................................................................. 36 4.3.1 Sensitivity Analysis: MPM (MATLAB) – DAKOTA Interfacing ........................... 37
4.4 Discussion and Future Work .................................................................................................. 39
5. CONCLUSIONS .............................................................................................................................. 41
6. REFERENCES (Sections 1 though 5) .............................................................................................. 43
7. ANL MIXED POTENTIAL MODEL WITH EXPERIMENTAL RESULTS:
IMPLEMENTATION OF NOBLE METAL PARTICLE CATALYSIS MODULE ...................... 46
7.1 Objectives and Context .......................................................................................................... 46
7.2 Mixed Potential Module and Surface Catalysis of Redox Reactions ..................................... 47
Used Fuel Degradation: Experimental and Modeling Report October 2013 xiii
7.3 Implementation of Noble Metal Particle Catalyzed Redox Reactions within the
Mixed Potential Module ......................................................................................................... 51
8. SUMMARY OF ELECTROCHEMICAL EXPERIMENTS ........................................................... 59
9. SUMMARY AND FUTURE WORK ON MPM ............................................................................. 60
10. REFERENCES (Sections 7 through 9) ............................................................................................ 62
11. GENERATING STRUCTURAL AND THERMODYNAMIC DATA FOR
GEOCHEMICAL AND USED FUEL DEGRADATION MODELS: A FIRST-
PRINCIPLES APPROACH ............................................................................................................. 63 11.1.1 Thermodynamic Properties of Uranyl Peroxide Hydrates Corrosion Phases
on Spent Nuclear Fuel: Studtite and Metastudtite ..................................................... 63 11.1.2 Structures and Properties of Layered Uranium(VI) Oxide Hydrates: Study of
Polymorphism in Dehydrated Schoepite ................................................................... 71
12. CONCLUSIONS .............................................................................................................................. 78
13. REFERENCES (Sections 11 through 12) ........................................................................................ 78
14. SUMMARY AND CONCLUSIONS ............................................................................................... 82
14.1 Concluding Remarks and Future Development ..................................................................... 84
15. APPENDICES .................................................................................................................................. 86
FIGURES
Figure S-1. Schematic diagram of the integration among activities for used fuel
degradation and the connection to a performance assessment model.
Experimental work (triangles) and first principles models (diamond) shown as
underpinning process models. .......................................................................................... 6
Figure 1.1. Components of a generic disposal system for used oxide fuel. .................................... 2
Figure 1.2. EBS coupled process phenomena and interrelations between process models
from other domains. ......................................................................................................... 5
Figure 1.3. Schematic of a fuel pellet cross section showing the relative locations of
radionuclide inventories for the gap, grain boundaries, fuel matrix, and noble
metal particles.. ................................................................................................................ 8
Figure 1.4. Schematic of a fuel pellet cross section for high BU UF showing the rim
region high-BU structure, transitional region, and core region ....................................... 9
Figure 1.5. Disposal system integrated process models (Freeze et al. 2013). ............................. 13
Used Fuel Degradation: Experimental and Modeling Report xiv October 2013
Figure 1.6. Schematic example of an idealized chronological evolution of the thermal,
hydrologic, mechanical, and chemical (THMC) conditions for a generic argillite
(clay/shale) disposal environment. Percentages in the hydrological part of the diagram
represent percent of water saturation in the media. ....................................................... 14
Figure 1.7. Schematic of potential parameter connections for fully embedded coupled fuel
degradation model with a performance assessment (PA) model. Solid arrows
unidirectional connections, whereas dotted arrows indicate bidirectional couplings
between subsystem models within the PA model. ......................................................... 17
Figure 2.1. Radiolysis model showing generation modified with a dose dependence term
in the irradiated zone and the diffusion zones across spatial regions. ........................... 20
Figure 2.2. Predicted conditional G-values for H2O2 with distance from the fuel surface
showing effect of external O2 at a fixed H2 concentration. ............................................ 23
Figure 2.3. Time dependent concentration of H2O2 and O2 at the surface with dose rates
of 40 rad/s, 80 rad/s, 137 rad/s, and 138 rad/s. .............................................................. 24
Figure 2.4. Steady-state concentrations of H2O2 at surface with dose rate for fixed initial
conditions, forward running steady-stated, and reverse running steady-state. .............. 24
Figure 3.1. Spatial diffusion grid for MPM showing individual calculation nodes as
vertical lines and summarizing key processes accounted for by the model .................. 26
Figure 3.2. Results from recent MPM runs investigating the sensitivity of fuel
degradation rate to changes in the G-value for H2O2 ..................................................... 32
Figure 4.1. Summary information flow diagram highlighting the coupling of radiolysis,
matrix, and instant release process modules within the FDM and PA. ......................... 33
Figure 4.2. Schematic diagram depicting the information flow for the MPM (Matlab) –
DAKOTA coupling. ....................................................................................................... 37
Figure 4.3. Concentration profile of U aqueous species computed by the MPM as a
function of temperature, dose rate, CO3--, and O2 concentrations. ................................ 40
Figure 4.4. Concentration profile of H2O2 computed by the MPM as a function of
temperature, dose rate, CO3--, and O2 concentrations. ................................................... 41
Figure 7.1. Summary information flow diagram showing the relationship of the FDM to
the system-level model and sub-models (modules) comprising the FDM. ................... 47
Figure 7.2. Key processes accounted for in the MPM. ................................................................ 49
Figure 7.3. Schematic diagram showing flow of electrons for surface catalyzed oxidation
of hydrogen .................................................................................................................... 51
Figure 7.4. Examples of time-dependent fuel corrosion potentials and corresponding
degradation rates calculated with the MPM for different dissolved hydrogen
concentrations with 1% NMP at the fuel surface. .......................................................... 55
Figure 7.5. Concentration profiles of hydrogen peroxide produced by alpha radiolysis as
a function of distance away from the fuel surface ......................................................... 56
Used Fuel Degradation: Experimental and Modeling Report October 2013 xv
Figure 7.6. Current densities for the key reactions over a range of hydrogen
concentrations ................................................................................................................ 57
Figure 7.7. Fuel corrosion potential and dissolution rate as function of hydrogen
concentration for two typical dose rates ........................................................................ 58
Figure 11.1. Schematic representation of the three-step computational approach used to
calculate the thermal properties of crystalline systems using first-principles
methods. ......................................................................................................................... 64
Figure 11.2. Crystal unit cells of (a) studtite, (UO2)O2(H2O)4 (space group C2/c, Z = 4),
and metastudtite, (UO2)O2(H2O)2 (space group Pnma, Z = 4) ...................................... 65
Figure 11.3. Thermal properties of studtite, (UO2)O2(H2O)4, calculated at constant
equilibrium volume at the DFT/PW91 level of theory. ................................................. 67
Figure 11.4. Thermal properties of metastudtite, (UO2)O2(H2O)2, calculated at constant
equilibrium volume at the DFT/PW91 level of theory .................................................. 67
Figure 11.5. Gibbs free energy of studtite calculated at constant atmospheric pressure at
the DFT/PW91 level of theory ....................................................................................... 68
Figure 11.6. Gibbs free energy of metastudtite calculated at constant atmospheric
pressure at the DFT/PW91 level of theory .................................................................... 68
Figure 11.7. Heat capacity of studtite calculated at constant atmospheric pressure at the
DFT/PW91 level of theory............................................................................................. 69
Figure 11.8. Heat capacity of metastudtite calculated at constant atmospheric pressure at
the DFT/PW91 level of theory. ...................................................................................... 69
Figure 11.9. Enthalpy functions and Gibbs energy functions of studtite and metastudtite
calculated at the DFT/PW91 level of theory.................................................................. 70
Figure 11.10. Crystal unit cells of the alpha-, beta- and (c) gamma phases of dehydrated
schoepite, UO2(OH)2, relaxed with DFT at the GGA/PBE level of theory ................... 74
Figure 11.11. Evolution of the computed volume and lattice parameters of α-UO2(OH)2,
as functions of the effective Hubbard parameter, Ueff.. ................................................. 75
Figure 11.12. Evolution of the computed U–O, O–H and O…
H bond distances in α-
UO2(OH)2, as functions of the effective Hubbard parameter, Ueff ................................ 76
Figure 11.13. X-ray diffraction pattern of α-UO2(OH)2. ............................................................. 77
Used Fuel Degradation: Experimental and Modeling Report xvi October 2013
TABLES
Table 2.1 Alpha particle G-values (Pastina and LaVerne, 2001) ................................................. 20
Table 2.2 Diffusion constants (Christensen and Sunder, 1996).................................................... 22
Table 3.1. Surface electrochemical reactions and bulk solution reactions tracked in the
MPM. ............................................................................................................................. 27
Table 4.1. Bounding constrains for input variables for DAKOTA.............................................. 38
Table 4.2. Simple DAKOTA Correlation Matrix among all inputs and outputs ......................... 39
Table 7.1. Parameter and variable inputs used for MPM runs ..................................................... 52
Table 11.1. Coefficients of the Haas-Fisher heat capacity polynomial Cp(T) for the
studtite and metastudite compounds .............................................................................. 70
Used Fuel Degradation: Experimental and Modeling Report October 2013 xvii
ACRONYMS AND ABBREVIATIONS
ANL Argonne National Laboratory
ATM Approved Testing Material
CV Cyclic Voltammetry
DOE Department of Energy (US DOE)
DR Dissolution rate
EBS Engineered Barrier System
EC European Commission
EIS Electrochemical Impedance Spectroscopy
FACSIMILE A computer program for modeling the kinetics of chemical systems
FEPs Features, events, and processes
FCRD Fuel Cycle Research and Development
FCT Fuel Cycle Technology
FDR Fractional Degradation Rate
FGR Fission gas release
FIRST Fast / Instant Release of Safety Relevant Radionuclides (EC project)
HBS High burnup structure
HLW High Level Waste
IRF Instant release fraction
IRM Instant Release Model
LWR Light water reactor
LPR Linear Polarization Resistance
MOX Mixed oxide fuel (e.g., U and Pu oxides)
MPM Mixed potential model
NMP Noble Metal Particle
NS Natural System
OC Open Circuit Corrosion
PA Performance assessment
PD Potentiodynamic
PNNL Pacific Northwest National Laboratory
PS Potentiostatic
PWR Pressurized water reactor
Used Fuel Degradation: Experimental and Modeling Report xviii October 2013
R&D Research and Development
RADFUEL Radiolytically-aged doped (RAD) synthetic nuclear fuels
RN Radionuclide
RM Radionuclide mobilization
ROK Republic of Korea
SA Surface area (m2)
SA Safety Assessment
SEM Scanning Electron Microscopy
SNF Spent Nuclear Fuel
SNL Sandia National Laboratories
THCM Thermal-hydrologic-chemical-mechanical (processes)
UF Used Fuel
UNF Used Nuclear Fuel
UFD Used Fuel Disposition
UFDC Used Fuel Disposition Campaign
UOX Uranium oxide fuel
WP Work package
Used Fuel Degradation: Experimental and Modeling Report October 2013 xix
MINERAL NAMES AND CHEMICAL FORMULAE
Meta-schoepite [(UO2)4O(OH)6](H2O)5
Meta-studtite UO4•2H2O
Schoepite [(UO2)8O2(OH)12](H2O)12
Studtite [(UO2) O2(H2O)2](H2O)2
UNITS
m micrometer
g grams
Gy Grays (100 Rads)
Kg kilograms
Kg kilograms uranium
M molarity, mole/liter
Mbq millibequerels
mg milligram
MTU Metric ton uranium
MWd megawatt-days
Used Fuel Degradation: Experimental and Modeling Report October 2013 1
1. MODEL OVERVIEW AND INTEGRATION
1.1 Introduction
Within the Used Fuel Disposition Campaign (UFDC) of the United States Department of Energy
Office of Nuclear Energy (DOE-NE), we have investigated used fuel (UF) degradation and
radionuclide mobilization (UFD&RM) and implemented/produced a set of models encompassing
radiolytic processes, UF matrix degradation, instant release fractions (IRF) of key radionuclides,
and first-principles atomistic models for UO2 and its potential corrosion products. The goals of
this collaborative effort (among three different national laboratories: Argonne National
Laboratory [ANL]; Pacific Northwest National Laboratory [PNNL]; and Sandia National
Laboratories [SNL]) are to enhance the understanding of UF degradation processes and the
technical bases for safety analyses in a range of generic disposal environments. In addition to
these modeling efforts, integrated experimental studies are being conducted at both ANL and
PNNL to evaluate and validate (and ultimately expand) process models for radiolytic phenomena
and UF matrix degradation in various geologic disposal conditions. Integration/coupling of these
process models into performance assessment models is one focus of SNL efforts within the
generic analyses of the Engineered Barrier System (EBS) for various repository environments.
As discussed below, the present work has produced a set of models for evaluation of used fuel
degradation as an initial step towards an enhanced coupled model of source-term processes.
1.1.1 Coupling the Mixed Potential and Radiolysis Models for Used Fuel Degradation
The primary purpose of this report is to describe the strategy for coupling three process level
models to produce an integrated Used Fuel Degradation Model (FDM). The FDM, which is
based on fundamental chemical and physical principals, provides direct calculation of
radionuclide source terms for use in repository performance assessments. The matrix
degradation model is used to calculate UO2 degradation rates by chemical and oxidative
dissolution mechanism based on electrochemical theory in the mixed potential model (MPM)
(Jerden et al. 2013). The radiolysis model (RM) is used to calculate steady state concentrations
of radiolytic species (Wittman and Buck, 2012) that participate in redox reactions modeled in the
matrix degradation model. The FDM source term includes radionuclides released from gap and
grain boundaries as quantified using an instantaneous release model (IRM) (Sassani et al. 2012).
The programmatic context for the work described in this report is shown in Figure 1.1. The
FDM uses input properties of the fuel waste forms and disposal environment to calculate the rate
of fuel degradation as the conditions at the fuel surface evolve over time. Radionuclides in the
fuel are mobilized at the same rate and made available for transport away from the waste
package. The FDM model provides the source term concentrations for radionuclides used in
reactive transport models of the disposal system.
Used Fuel Degradation: Experimental and Modeling Report 2 October 2013
Figure 1.1. Components of a generic disposal system for used oxide fuel (adapted from Freeze et
al. 2010). The red circle identifies the processes covered by the models described in this report.
Additionally, an overview of the strategy for incorporating the FDM into performance
assessment models is also described in this first section. The strategy is given as part of the of
the model development in each area given as context summarizing the connections among all
the modeling activities.
1.2 Background and Overview of Models
The Used Fuel Disposition Campaign (UFDC) supports the Fuel Cycle Technology (FCT)
Program established by the United States Department of Energy Office of Nuclear Energy
(DOE-NE). The mission of the UFDC is to identify alternatives and conduct scientific research
and technology development to enable storage, transportation and disposal of used fuel (UF)
and wastes generated by existing and future nuclear fuel cycles. This article covers research
activities on engineered barrier system (EBS) model development in the UF degradation and
radionuclide mobilization (UFD&RM) activities in support of the generic EBS analyses, tool
development, and model integration into performance assessment (PA) model (Sassani et al.,
2012).
Currently, performance models for four generic disposal environments (i.e., repositories in salt,
granite, and clay/shale, and deep borehole disposal in various media) include constraints on
radionuclide release from UF based on sampled distributions for the general ranges of
fractional degradation rates taken from the literature. These generic models further constrain
radionuclide mobilization away from the UF using published solubility-limited radionuclide
concentrations for those radioelements expected to be reprecipitated under local conditions
within the EBS. The potential instant release fractions (IRF) of key radionuclides have not
been directly incorporated into these four generic approaches, which are currently being
subsumed into performance assessment models.
Used Fuel Degradation: Experimental and Modeling Report October 2013 3
For the next stage of performance assessment (PA) model development, the current UFD&RM
work provides process-model-based fractional degradation rates for UF that account more
directly for the effects of the major chemical variables in the source-term model (Sassani et al.,
2012). Investigating UFD&RM has led to implementation of process models for (a) UF matrix
degradation rates (the Mixed Potential Model - MPM) and (b) UF radiolytic processes and the
major radiolytic species production (the Radiolysis Model – RM). In addition, constraints for
the IRF of key radionuclides have been provided for use in PA, and first-principles atomistic
models for UO2 and its potential corrosion products have been developed. The MPM and the
RM are to be coupled for use within performance assessment model evaluations of the source
term in the post-closure environment. Implementation of these process models into
performance assessment models facilitates enhanced coupling to chemical variables, and
expected thermal and pressure variations, as well as more explicit treatment of phase evolution.
Moreover, two sets of distributions providing constraints for the fast/instant release fraction of
radioelements (Cs, I, Tc, Sr, C and Cl) based on literature values are provided for sampling
within the performance assessment models. Furthermore, first-principles models for the bulk
chemical properties and surface chemistry of UO2, as well as for the structures of studtite and
metastudtite, provide a rigorous methodology for evaluating/validating continuum scale
models of UF degradation, and facilitate the enhanced mechanistic analysis of processes
governing fuel degradation.
1.2.1 Used Fuel degradation processes within the engineered barrier system
The generic EBS analyses (Jové Colón et al., 2012) entail the evaluation, tool development,
and integration with performance assessment models, including the study of used nuclear fuel
degradation. The latter ultimately determines calculated radionuclide releases beyond the
confines of the nuclear fuel and waste container. Integration of EBS models with performance
assessment models is an effort that evolves in parallel with PA and safety assessments (SA),
and repository barrier processes (and sub-processes) model development. More advanced
analysis of generic disposal concepts requires the accurate understanding of processes leading
to radionuclide releases from the EBS, specifically at the barrier interface between fuel
assemblies and containment structures. Multilayered EBS concepts and related materials
evaluated by the UFDC seek to provide the necessary level of confidence to ensure safe and
robust long-term waste isolation.
However, it is sensible to anticipate that waste containment failure would affect some canisters,
therefore exposing fuel to interactions with subsurface fluids and eventually leading to
radionuclide release. Given the importance of such processes to long-term disposal system
performance, the main objectives (Sassani et al., 2012) of the FY2013 UFD&RM effort are:
Data analysis and generation of statistical distributions to represent the IRF of
radionuclides from the nuclear fuel.
Implementation/development of a rigorous and comprehensive RM to evaluate the
U-H2O-CO2 system (expanding to other chemical components as needed, e.g., Cl
for salt systems).
Implementation/development of a predictive model capability for used nuclear fuel
matrix degradation rates based on electrochemical and thermodynamic principles
(i.e., the mixed potential model, or MPM).
Used Fuel Degradation: Experimental and Modeling Report 4 October 2013
Use of computational methods and approaches based on first principles to study the
structures of uranium-bearing oxides and their degradation products (Weck et al.,
2012; 2013).
Strategy for coupling the RM and MPM into used fuel degradation model (FDM)
and preliminary development of an integrated framework strategy for passing
information between EBS process models and the performance assessment models
(Sassani et al.,. 2012; 2013).
1.2.1.1 Engineered Barrier System Interfaces
The generic evaluation of EBS performance in geologic repositories requires an all-inclusive
analysis of key processes (and sub-processes) affecting the isolation capacity of engineered
barrier domains emplaced within the considered host media. Jové-Colón et al. (2012) described
the importance of the analysis of Thermal-Hydrological-Mechanical-Chemical processes
common to different EBS design concepts for various materials, local environment, and
specific interactions as illustrated in Figure 1.2. Also depicted in this figure are the connections
from UF degradation and radionuclide mobilization (UFD&RM) processes to the EBS. Used
fuel degradation represents a set of coupled processes defined mainly by interactions between
nuclear fuel and fluids in the EBS that ultimately provides the radionuclide source-term.
It should be noted that fuel cladding is currently treated as the interface between the UFD&RM
and EBS. The task of integrating process models to describe cladding evolution/degradation
with those of the UF degradation will be a growing focus of the UFD&RM tasks once the
current models are integrated into performance assessment models. A summary report
(Sassani, 2011) provided an overview of the modeling and experimental tasks for FY2011 in
UFD&RM and outlined the goals of this work for FY2012. A more recent report (Sassani et
al., 2013) describes the current model implementations and provides a conceptual framework
for coupling and integration of those models within the performance assessment models. The
major conceptual approach for these modeling efforts is described in the next section.
Used Fuel Degradation: Experimental and Modeling Report October 2013 5
Figure 1.2. EBS coupled process phenomena (center) and interrelations between process models
from other domains (from Fig. 1.1-1 in Sassani et al., 2012).
Used Fuel Degradation Process Models
Fluxes from Waste Package
Coupled ProcessesThermalHydrologicalMechanicalChemical
Far-Field Process Models
Far-Field / Near-Field Fluxes
Ne
ar-F
ield
En
viro
nm
en
t Barrier DomainsBackfill / BufferCanister / Liner
Seals
Heat Flow (Conduction)
Solid
Sorption
Mineral
DissolutionPrecipitationHeat & Liquid Flux
Solute Flux(diffusion, advection)
Liquid
LiquidEvaporation
LiquidCondensation
Gas Flux(diffusion, advection)
Heat Flux
Gas
Pressure
Pressure
Diffusion
Used Fuel Degradation: Experimental and Modeling Report 6 October 2013
1.2.2 Used Fuel Degradation and Radionuclide Mobilization Concepts and Models
Once the cladding around UF is breached in a failed waste package, the UF will be exposed to
ingress of water and/or humid air. The radionuclide mobilization from such exposed UF can
depend on the type of cladding breach and on the progression of cladding degradation
following the initial cladding breach. Several hypothetical scenarios for the evolution of the
state of a fuel rod following breach of its cladding are plausible. In one case, the corrosion of
the fuel and precipitation of alteration products in a breached fuel rod could quickly lead to
axial splitting, or “unzipping,” of the cladding. Another case is that the precipitating alteration
phases will fill the gap and fracture openings and, as a result, limit the rate of further fuel
degradation and radionuclide release. A further possibility is that cladding corrosion from the
fuel-side will cause additional cladding degradation and exposure of the fuel pellet fragments
(Cunnane et al., 2003). Because the specific effects of cladding failure are planned to be
evaluated and integrated into the models of UF degradation in the future, this work focuses on
an idealized case where the breached cladding does not influence the fuel matrix degradation
or radionuclide mobilization.
Because some radionuclides are dissolved in the UO2 matrix grains, their releases are
controlled by the degradation rate of the UF matrix itself (e.g., Pu, Np). In addition to these
solid solution radionuclides, some other radionuclide releases may be controlled, in part, by the
matrix degradation rate. These include fission products present in the inaccessible grain
boundaries (i.e., those grain boundaries occluded to fluid until the fuel matrix alters enough to
provide fluid access). Some fission products occur as discrete phases (e.g., the five-metal alloy
particles, or epsilon phase) in both the matrix grains and in the inaccessible grain boundaries.
These portions of the inventory are referred to collectively as the “matrix inventory” because
matrix degradation is required prior to release of these radionuclides. The matrix inventory
does not include radionuclides located within the accessible grain boundaries (see below). Note
that the epsilon phase particles seem to corrode slower than the fuel matrix (Sassani, 2011;
Sassani et al., 2012), and therefore release of radionuclides from these noble metal phases may
lag the degradation of the matrix itself.
Other than the radionuclide inventories whose releases are controlled by UF matrix
degradation, there are portions of the inventories of fission gases and of more volatile
radioelements (e.g., cesium, iodine, and technetium) that are released virtually instantaneously
upon cladding breach (i.e., the instant, or fast, release fractions-IRF). This IRF is mostly fission
products that have migrated out of the matrix during in-reactor operations and accumulated as
gases or minor condensed phases along the fuel gap (i.e., the interface between the pellets and
the cladding), the rod plenum regions, and in the readily accessible pellet fractures and grain
boundaries (this includes epsilon phase particles). Within this work, these locations are
collectively referred to as the “gap region” that contains the inventory of radionuclides that are
released independently of the UF matrix degradation rate.
Used Fuel Degradation: Experimental and Modeling Report October 2013 7
On the basis of the above discussion, the radionuclide inventory in UF can be subdivided in
this manner:
• The IRF inventory (includes fission gases) comprised of radionuclides located in
– The rod plenum regions (e.g., Kr and Xe)
– The fuel gap (between pellet & cladding; Figure 1.3)
– The accessible grain boundaries/pellet fractures (Figure 1.3)
• The matrix inventory (Figure 1.3) that includes the UF matrix itself and radionuclides
located within
– The matrix grains as solid solutions
– The inaccessible grain boundaries and fractures
– The epsilon phase particles both (a) enclosed in the matrix and (b) within the
inaccessible grain boundaries (NOTE: the epsilon particles undergo their own
degradation rate once exposed by matrix degradation)
These inventories, the major rate limiting processes (e.g., matrix degradation, noble metal
particle degradation), and radionuclide mobilization processes and models for each of these
fractions are summarized below.
Instant Release Fractions
Within the grain-boundary region of the fuel pellet, radionuclides may be readily releasable
(accessible grain boundary inventory), or may be inaccessible (the inaccessible grain boundary
inventory – see Figure 1.3). This latter portion would remain unreleased until degradation of
the UF matrix occurs to the point where these grain boundaries are now exposed to fluids.
Mobilization of the inaccessible grain-boundary inventory requires prior degradation of the
matrix grains to make accessible these initially inaccessible grain boundaries in the UF.
Degradation of the grain boundaries may occur due to the effects of helium production from α-
particle decay on the mechanical stability of the grain boundaries (Ferry et al., 2006) or from
preferential corrosion at/along the grain boundaries. Although this is straightforward in
concept, delineation of the accessible grain boundaries from the inaccessible ones is not a
simplistic task and methods of measuring the grain boundary inventories (e.g., grinding of
samples) tend to capture the total rather than discriminate between the two (BSC, 2004; Roudil
et al., 2007). Similar complications of discrimination apply also to the accessible versus
inaccessible fractures within a used fuel pellet.
Because the initial fraction of inaccessible grain boundaries and the progression of the grain
boundary corrosion within geologic disposal systems are not well understood, it has been
common for the entire grain boundary inventory to be conservatively assumed to be released
instantaneously (i.e., as part of the IRF) upon water ingress into the breached fuel rods (BSC,
2004; Johnson et al., 2005). Additional empirical data obtained from long-term fuel corrosion
testing indicates that oxidative dissolution of the fuel matrix is a general corrosion process and
does not exhibit substantial preferential corrosion along the grain boundaries (Une and
Kashibe, 1996; BSC, 2004). This suggests that the inaccessible grain boundary inventory
would be mobilized at a rate similar to radionuclides within the fuel matrix, and could
Used Fuel Degradation: Experimental and Modeling Report 8 October 2013
therefore be released in proportion to the matrix degradation. Further data for distribution of
inaccessible grain boundary radionuclide inventory and advanced understanding of grain
boundary degradation in UF would facilitate this approach, particularly for high burnup (BU)
UF, which has additional structural changes/complexity as BU increases (Figure 1.4).
Figure 1.3. Schematic of a fuel pellet cross section showing the relative locations of radionuclide
inventories for the gap, grain boundaries, fuel matrix, and noble metal particles. Also shown
schematically are the general locations of accessible and inaccessible grain boundaries.
For the purposes of this work, a transition point to high BU UF is defined as occurring at 45
MWd/kgU such that any UF that has a BU >45 MWd/kgU is referred to as high BU. This is in
part based on the observation that the amount of fission gas release (FGR; e.g., Kr and Xe) for
LWR UF depends more strongly on the magnitude of BU for fuels above 45 MWd/kgU (e.g.,
see Figure 1 in Johnson et al., 2012). Besides containing more fission products, such high BU
UF exhibits distinct structural changes at the pellet rim that are driven by locally increased 239
Pu content. The increased 239
Pu causes elevated local BU (factor of 2 to 3) that results in a
finer-grained structure with higher closed-porosity (containing fission gases) that occurs as a
rim layer (Johnson et al., 2005; Serrano-Purroy et al., 2012). This rim layer of high-BU
structure (Figures 1.1-1.4) is noticeable in UF starting around a BU of 40 MWd/kgU (Johnson
et al., 2005). The rim region grows progressively thicker as BU increases (and with increase in
other irradiation history parameters—
De Pablo et al., 2009) and is separated by a transitional
region from a core lacking high-BU structure (Serrano-Purroy et al., 2012).
Models that have been developed (BSC, 2004; Johnson et al., 2005) for mobilization of the gap
and grain-boundary inventories assume conservatively that they are instantaneously released
(i.e., the IRF) when groundwater contacts the UF through the breached cladding for even a
pinhole failure. As UF BU increases, fission products are more abundant and FGR is observed
to increase, so IRF models are either correlated (Johnson et al., 2005) to BU and FGR, or at
Used Fuel Degradation: Experimental and Modeling Report October 2013 9
least account for a substantial range (BSC, 2004) of these parameters. One set of IRF model
values (for Sr, I, Cs, and Tc; BSC, 2004) covers a UF FGR range of 0.59 to 18% FGR. The
IRF distributions generated for that model simply span the entire range of FGR evaluated,
which represents a BU values up to about 50 MWd/KgU, and include the variability across the
range to capture conceptual uncertainty in this parameter. It is recommended that the BSc
(2004) distributions be used to analyze IRF in PA with consideration of the uncertainty for
fuels of BU below about 50 MWd/KgU. As discussed in that work, comparison to additional
literature data indicates that the distributions for Sr and Tc release may not be conservative
(BSC, 2004). However, BSC (2004) also noted that both Tc and Sr are radioelements that can
be affected strongly by matrix dissolution within testing data, such that the values may be
inadvertently high in some studies. Using the BSC (2004) distributions for fuels above 50
MWd/KgU is not recommended because they are not demonstrably conservative compared to
the pessimistic estimate model values from Johnson et al. (2005 - discussed below) for higher
BU values.
Figure 1.4. Schematic of a fuel pellet cross section for high BU UF showing the rim region high-
BU structure, transitional region, and core region (after Fig. 1, Serrano-Purroy et al., 2012).
An extensive evaluation of IRF for UO2 (and mixed oxide - MOX) fuels by Johnson et al.
(2005) has been conducted based on correlations of fission product (e.g., Cs, Sr, I, Tc, and C)
leaching data with FGR (e.g., Xe). Johnson et al. (2005) combined those measurements with
FGR correlations as a function of BU to extrapolate IRF data for value estimates to higher BU.
Johnson et al. (2005) produced best estimate and pessimistic estimate IRF values for UF as a
function of the fuel BU. These estimates are indicated to be reliable for low to moderate BU
UO2 fuels, and less certain for the higher BU fuels for which experimental leaching data are
Used Fuel Degradation: Experimental and Modeling Report 10 October 2013
sparse (Johnson et al., 2005). However, additional studies of high BU fuels, some explicitly
analyzing the UF rim regions and cores separately (Roudil, et al., 2007; De Pablo et al., 2009;
Serrano-Purroy et al., 2012) suggest that these model values may be conservative estimates of
the IRF (especially Tc).
Because of the need to evaluate the variability of UF BU in the source-term of performance
assessment, it is recommended that the best- and pessimistic-estimate values of Johnson et al.
(2005) be used to define the minimum and maximum values, respectively, for uniform
distributions at each BU for which they are listed. This will allow evaluating the major BU
variation for UF up to 75 MWd/KgU. Linear interpolation between listed BU values should be
used to generate distributions for intermediate BU levels, but extrapolation beyond the
maximum BU given by Johnson et al. (2005) should not be performed.
Johnson et al. (2005) utilized direct consideration of both FGR and BU for constructing their
model values. In addition, Johnson et al. (2012) pointed out that high FGR in some fuels
(specifically 11% and 18% in ATM-106 with BUs of 46 and 50 MWd/KgU, respectively) is
not due to higher BU, rather it is likely due to original lower density of the manufactured fuel
providing higher open porosity. This would mean that simply using estimates dependent solely
on FGR could lead to overestimates of the IRF in such cases. Mobilization models for the IRF
(which estimate the fraction of the inventory of key radionuclides that are instantly released
upon cladding breach) could be parameterized to include changes that may occur over time
throughout the post-closure period as a result of additional migration of radionuclides within
the UF structure (Johnson et al., 2005; Poinssot et al., 2005). These effects are currently
viewed as second order and are probably captured by the more conservative values
recommended above.
Matrix Degradation Rate
The major elemental components comprising the matrix of the UO2 and MOX UF are U and
Pu. Minor elemental constituents (e.g. Pd and other noble metal fission products) may also
influence the corrosion of the fuel matrix, for example by catalyzing cathodic reactions. When
the fuel matrix is corroding, the inherent corrosion potential of the primary mass of the oxide
grains (UO2 and MOX) controls and buffers the electrochemical conditions at and near the
corroding surface. Many of the radioelements in UF (e.g. U, Pu, Np, Tc, I) are multivalent
elements. The valence of the ions produced in the corrosion process depends on the corrosion
conditions (e.g., potential and pH) at the surface of the corroding UF matrix. Because oxidation
and dissolution of U and Pu produces high valence cations (oxidation states higher than 4),
following their dissolution these ions undergo extensive hydrolysis and precipitate to form rind
layers on the UF. Other multivalent radionuclides may only be present in their lower oxidation
states during the fuel matrix corrosion process if the corrosion potential of the fuel matrix in its
disposal environment is sufficiently low. Consequently, the radionuclides mobilized in lower
valence (and less soluble) states may be retained in the rind layer unless they are subsequently
oxidized to a higher oxidation state and dissolved into the bulk solution.
The oxidation of the UF surface within reduced disposal environments may be driven by
radiolytically generated oxidizing species. Species such as H2O2 may be the dominant oxidant
produced by alpha radiolysis at long times (Sassani et al., 2012; Wittman and Buck, 2012).
However, in these environments; generation of hydrogen gas from metal corrosion with water
may provide a source of reductants for reaction with such oxidants. It is possible that such
Used Fuel Degradation: Experimental and Modeling Report October 2013 11
reactions may protect the UF surface from oxidative dissolution and may be facilitated by the
cathodic and/or catalytic behavior of epsilon phase particles in the UF itself (Jerden et al.,
2013). For such a case, simple solubility-driven dissolution of the UF would provide much
slower degradation of this waste form in reduced disposal environments. Quantification of
these processes and implementation/extension of process models to account for them has been
a focus of the UFD&RM activities (Sassani et al., 2012; Wittman and Buck, 2012; Jerden et
al., 2013). These models are summarized here for the context of incorporating them into PA
models, with detailed descriptions of the process models given in Sections 2 and 3, and the
strategy for coupling them given in Section 4.
Radiolytic products exert strong effects on UO2 dissolution at the solid-aqueous interface.
Therefore, the effects of radiolysis on solution redox speciation at this interface need to be
considered within UO2 corrosion models. Initial RM implementation (Wittman and Buck,
2012) is based on the kinetics of Christensen and Sunder (2000). Within the water system,
H2O2 becomes the dominant radiolytically generated oxidant. Uncertainty in model parameters
and reaction mechanisms was analyzed to quantify the sensitivity of dissolution rate to RM
parameters and to identify the largest uncertainties. The RM has been verified using additional
reaction sets from Poinssot et al. (2005) and Pastina and LaVerne (2001). Additionally,
experiments are being performed to reduce model uncertainties and validate model concepts
(Sassani et al., 2012). These experiments include studies of radiolytic H2O2 production and
thermal degradation rates in solution and studies using synthetic fuels to evaluate future alpha
radiolytic conditions in disposal systems (Sassani, 2011; Sassani et al., 2012). Such testing will
provide validation studies for the RM and/or parameter values to the UFD&RM process
models. The RM is being expanded to include heterogeneous environments consisting of solid-
water layer-gas phase, and to include chloride for evaluating a generic salt environment.
The overall objective of this work was to implement a predictive model for the degradation of
used uranium oxide fuel that is based on fundamental electrochemical and thermodynamic
principles. This objective was achieved (Sassani et al., 2012; Jerden et al., 2013) by the initial
MPM implemented in the form of a computational tool that is based on the Canadian-mixed
potential model for UO2 fuel dissolution (King and Kolar, 1999; 2003; Shoesmith et al., 2003).
This initial implementation extends the Canadian version to include hydrogen oxidation at the
UF surface with provisions to include reactions catalyzed by noble metal particles present at
the fuel surface. The MPM was verified by reproducing published results from the Canadian
model and sensitivity analyses1 were used to determine which model parameters and input
variables have the largest effect on degradation rate. As part of the work at ANL, experimental
methods have been developed to measure electrochemical and reaction kinetic parameters to
support modeling investigations and to quantify epsilon particle effects on matrix degradation
for inclusion in an updated MPM (for details see Jerden et al., 2012, FCRD-UFD-2012-000169
and Jerden et al., 2013 FCRD-UFD-2013-000057; and Sassani et al., 2012 for general
discussion).
In addition to the process model developed for matrix degradation, studies of the mechanistic
behavior of the corrosion products of UO2 and the energetics of UO2 bulk and surface reactions
have been performed to compliment the continuum model for matrix degradation. A
computational first-principles study of the structures of the uranyl peroxide hydrates studtite
and metastudtite documents their structures obtained from total energy calculations using
Used Fuel Degradation: Experimental and Modeling Report 12 October 2013
density functional theory (Weck et al., 2012). These computational results are in very good
agreement with those characterized by experimental X-ray diffraction methods. Such work
tests this computational tool to quantify their thermodynamic properties for use in similar
studies of UO2 bulk and surface chemistry (Weck et al., 2013). Such first-principles studies
will serve to provide parameter constraints for process models of UF degradation and to supply
validation comparisons.
1.2.3 Integration into the performance assessment models
Performance assessment models provide a common conceptual and computational framework
for the simulation of coupled thermal-hydrologic-chemical-mechanical-biological-radiological
processes that govern the behavior of nuclear waste disposal systems (Freeze and Vaughn,
2012). Within the common performance assessment models framework, a range of disposal
system alternatives (combinations of inventory, EBS design, and geologic setting) can be
evaluated using appropriate model fidelity that can range from simplified reduced-dimension
representations running on a desktop computer to complex coupled relationships running in a
high-performance computing environment (see e.g., Fig. 2.1-1 in Sassani et al., 2012). It
should be noted that used fuel degradation and related EBS processes are part of the PA model
integration structure envisioned in the Generic Disposal System Modeling (GDSM) and
Advanced Disposal System Modeling (ADSM) (Freeze et al., 2013). For example, Figure 1.5
shows the “Source Term and EBS Evolution” (top-left) box delineating waste form (WF)
degradation as part of the breakdown of key source term and EBS coupled processes within the
PA integration scheme.
The EBS is represented with a number of major barriers of various types depending on disposal
environment, as well as with various waste forms, including UF that is the primary topic of this
article. Most of the models implemented currently in the performance assessment models for
EBS are more idealized than fully coupled, but the plan is to augment or replace those simpler
models with more comprehensively coupled process models as the work progresses. The
models for UF degradation processes are expected to be some of the earliest augmentations.
Consideration of the context in the evolution of the post-closure environment is needed when
applying the process models for used fuel degradation either on their own, or within the PA
models. Temporal evolution of both the natural and engineered barriers in the system will have
thermal, hydrologic, chemical, and mechanical changes driven by the system conditions as well
as by the placement of the waste forms in that system. A stylized example of the chronological
evolutions of such system conditions is shown in Figure 1.6 for an argillite (clay/shale)
disposal environment. This figure is based on a similar chronological description for THMC
coupled processes in an argillite repository for the TIMODAZ project described in Yu et al.
(2010). The thermal evolution is driven primarily by the radioactive decay of the used fuel and
provides coupled effects within the three other process areas (e.g., drying of the immediate
vicinity). Note that the chemical conditions are those imposed from the evolution of the natural
system and the engineered barriers excluding the waste form itself. The models discussed
within this report are those that would evaluate additional chemical aspects of the fuel either
generated from the radiolytic effects of the used fuel on any water (relevant only once there is a
breach of both waste package and cladding) or vapor, as well as bulk chemical changes due to
the dissolution/degradation of the fuel itself. In general, the point in time of these failures will
be out in time after the thermal perturbation of the system has decreased. This is just one
Used Fuel Degradation: Experimental and Modeling Report October 2013 13
example of such temporal changes for one possible generic disposal system and the process
models in this report are developed to be able to address the range of possible conditions,
focusing primarily on the dominant conditions expected for fuel degradation during post
closure.
Figure 1.5. Disposal system integrated process models (Freeze et al. 2013).
Used Fuel Degradation: Experimental and Modeling Report 14 October 2013
Figure 1.6. Schematic example of an idealized chronological evolution of the thermal,
hydrologic, mechanical, and chemical (THMC) conditions for a generic argillite (clay/shale)
disposal environment. Percentages in the hydrological part of the diagram represent percent of
water saturation in the media.
Years 1 10 100 1000 10000 100000 1E+06
Temperature (T)
Swelling Clay Plug
0% ~90%
0% >90%
0% <70%
0% <70%
0% <70%
Oxidizing Conditions Reducing Conditions
Overpack Corrosion
Hydrogen Production from Corrosion
Primary Package Corrosion
Chemical (C)Plug / Concrete
Degradation
Alkaline Plume in Near-Field
Bentonite / Cement Plug
Wasteform Degradation, RN Release
Sorption, Colloid Formation/Transport
~80 - ≤97%
Concrete Plug
>97%
Moderate RH After 1000 years
~80 - ≤97%
Moderate RH After 1000 years
Glass Dissolution
Outer Metal Sleeve Corrosion
Mildly Reduced
Mechanical (M) Overpack & Canister Rupture
~80 - <97%
~80 - <97%
~80 - <97%
Water in Contact with WPsNo water contacting WPs
WP Breach
Drift Wall / Liner~90 - ~100%
Clay Outer Barrier~80 - ~100%
Clay Inner Barrier~80 - ~100%
Hydrological (H)
70%
Liner Rupture Variation in Argillite Creep Rates in the Near-Field
~80%Micro-cracked Argillites ~100% ~100%~80%
Thermal Pulse Temperature Decrease Site Geothermal Gradient
~90 - ~100%
~90 - ~100%
>90%
>90%
~80% - ~100%
High RH After 1000 years
>97%
High RH After 1000 years
>97%
High RH After 1000 years
Dryout Period
Dryout Period
Dryout Period
Dryout Period
Dryout Period
Cell Closure Repository Closure
Post-Closure Period
Used Fuel Degradation: Experimental and Modeling Report October 2013 15
For the source-term models of the four generic disposal environments, the implementations are
generally simplified. For example, in Clayton et al. (2011) the generic salt source-term model
is described as follows:
Waste form degradation is assumed to release radionuclides into a large uniformly mixed
container representative of the source-term water volume. The source-term water volume is
obtained by multiplying the source-term bulk volume by its porosity. The dissolved
concentrations of radionuclides in the source term mixing cell are then calculated based on
the mass of radionuclides released from the waste form, the source-term water volume, and
the radionuclide solubility. … As the model matures and information becomes available,
more realistic representations of the processes will replace this initial simplified approach.
Within that generic salt source-term model, two components relate directly to the degradation
of UF: (a) waste form degradation, and (b) solubility of key radioelements for the performance
assessment models analyses. This UFD&RM work is focused currently on providing
augmented process models for part (a), specifically for UF as a waste form. The salt source-
term representation of the waste form degradation in Clayton et al. (2011) includes the source-
term, degraded waste form, and primary engineered barriers components. These two simplified
aspects of that approach could be updated based on the models in this work. Such update
would mean that instead of the generic source term having “No gap/grain boundary fraction”
and simply sampling a distribution for “Fractional Degradation Rate”, there would be an
instant release fraction included (sampled based on the distributions described above) and the
fractional degradation rate could be calculated using the model instead of sampled.
The primary connection into the current performance assessment models for the UFD&RM
models is the fractional degradation rate (FDR) parameter, which is currently sampled from a
distribution as indicated above. This primary coupling allows for development of more
process-based models that are able to supplant the FDR distribution by supplying that
parameter directly as a result of the process model. This is the initial connection that is needed
for implementation of the UF MPM described above. In addition, a second connection could be
generated to represent the instant release fraction. Sampling of the IRF distributions within the
PA model would be done similar to the current sampling of the FDR distribution to describe
the fast/instant release fraction radionuclides that are mobilized instantly at the time of
cladding breach. The distributions for the IRF would only need to be sampled at the initiation
of UF degradation for each fuel rod represented as having a breach in its cladding.
A coarse connection to chemical environment (defined in the performance assessment models
and needed as input to the UFD&RM models) exists currently in the form of the four generic
disposal environments. At present this is sufficient as the UFD&RM models discussed herein
are developed for granitic reducing environments and explicit coupling to chemistry variation
is expected to be an ongoing enhancement, with a primary target of extending the model
applicability into clay/shale and deep borehole environments (expansion to specific brine
environments appropriate to salt systems will be undertaken in the future if needed). This is
also the case for thermal and pressure dependencies that will be further incorporated into the
UFD&RM models and will capture essential environment and temporally-changing conditional
parameters. It is expected that as these enhanced models are incorporated into the performance
assessment models, expanding explicit environment/chemical variability coverage within the
models will become more efficient.
Used Fuel Degradation: Experimental and Modeling Report 16 October 2013
Our general strategy for integrating process models with each other, and within the
performance assessment models, is to identify initially the major feeds among the process
models (given in detail in Section 4) and from the process models to performance assessment
models (see below for discussion of connections). For coupling into performance assessment
models, our approach begins with the direct, though idealized, interface connections that exist,
with further couplings added as the process models themselves become more highly coupled.
The ultimate tool for connection with the PA models in intended to be a single coupled process
model, or fuel degradation model FDM – see Section 4), for analyzing the fractional
degradation rate of used fuel within the PA Models. Note that even after coupling, the RM and
MPM process models can be used individually for sensitivity and uncertainty analyses as well.
One more simplistic approach to coupling to the PA models would be to use the RM and MPM
(or even the FDM) process models to generate a set of histories based on radiation and thermal
output of the fuel through time. This could be done initially for each generic disposal chemical
environment (e.g., granitic groundwater or clay/shale), and simply directing the PA model to
select the appropriate set of histories to sample depending on which environment was being
analyzed.
Such a unidirectional coupling may only be an initial stage of coupling the FDM with PA
models and the approach could progress to the direct incorporation of the coupled process
model into the PA models. Such a thorough coupling would entail passing water compositional
parameters (potentially from other internal chemistry models) to the FDM, which would
analyze the UF degradation in this environment and provide the fractional degradation rate for
those specific water compositions. This would be a bidirectional coupling example. Further
coupling of the FDM into the PA model with a full suite of coupled thermo-hydro-chemical
processes would allow a fully coupled feedback where, in addition to the fractional degradation
rate being provided to the performance assessment models, the change to water composition
based on the UF degradation could be supplied as well. The potential connections between the
FDM and the other PA model subsystems are shown in Figure 1.7. Such a staged
developmental strategy facilitates incorporation of process-level detail as it is available and
permits an evolving level of complexity to be incorporated in a deliberate manner.
Used Fuel Degradation: Experimental and Modeling Report October 2013 17
Figure 1.7. Schematic of potential parameter connections for fully embedded coupled fuel degradation model with a performance
assessment (PA) model. Solid arrows unidirectional connections, whereas dotted arrows indicate bidirectional couplings between
subsystem models within the PA model.
Used Fuel Degradation: Experimental and Modeling Report 18 October 2013
1.2.4 Summary
The contributions presented in this manuscript are being accomplished via a concerted effort
among three different national laboratories: SNL, ANL and PNNL. This collaborative
approach includes experimental work, process model development (including first-principles
approaches) and model integration—both internally among developed process models and
between developed process models and PA models. The main accomplishments of these
activities are summarized as follows:
Delineation of constraints for the IRF from the nuclear fuel implemented in two sets of
distributions: (a) triangular distributions representing minimum, maximum, and mean
(apex) values for LWR UF with BU at or below 50 MWd/KgU, and (b) uniform
distributions as a function of BU representing instantaneous radionuclide releases for
UF with BU up to 75 MWd/KgU.
Computational development and implementation of a radiolysis model using a
comprehensive set of radiolysis reactions to better account for potential solution
compositions to be encountered in repository environments (Wittman and Buck, 2012).
The current model (Section 2) allows for heterogeneous CO2 speciation thus accounting
for the presence of HCO-3. Comparisons of modeling results are in good agreement
with those reported in other studies.
Computational implementation and verification/validation of the Canadian mixed
potential model for UO2 fuel corrosion in the initial mixed potential model (MPM -
Jerden et al., 2013). This MPM (Section 3) is based on the fundamental electrochemical
and thermodynamic properties described by interactions at the fuel – fluid interface and
captures key processes such as hydrogen oxidation and the catalysis of
oxidation/reduction reactions by noble metal particles on the fuel surface (epsilon
phases).
A computational first-principles study of the structures of the uranyl peroxide hydrates
studtite and metastudtite (Weck et al., 2012). The structures obtained from total energy
calculations using density functional theory are in very good agreement with those
characterized by experimental X-ray diffraction methods. Such work tests this
computational tool to predict the phase stability of UO2 corrosion products and quantify
their thermodynamic properties for use with similar studies of UO2 bulk and surface
chemistry (Weck et al., 2013).
Development of an idealized strategy for model integration with PA approaches to
analyze generic disposal environments (Section 1.2.2). However, it is an ongoing task
to delineate in detail how these process models will couple to other EBS process
submodels within the PA model for generic evaluations of the safety case.
Advanced strategies for coupling the RM and MPM into a single tool for use in
analyzing the matrix degradation rate (fractional and absolute) of used fuel (Section 4).
Identification of parameters needed to couple the codes together as well as four
strategies for implementing the coupling are given in detail in Section 4.
Used Fuel Degradation: Experimental and Modeling Report October 2013 19
2. SUMMARY OF RADIOLYSIS MODEL
The radiolysis model (RM) calculates the concentration of species generated at any specific time
and location from the surface of the fuel (Wittman and Buck, 2012). The model will be used as a
component in a total system model for assessing the performance of UNF in a geological
repository. The total system model will account for time-dependent phenomena that may
influence UNF behavior. One major difference between used fuel and natural analogues,
including unirradiated UO2, is the intense radiolytic field. The radiation emitted by used fuel can
produce radiolysis products in the presence of water vapor or a thin-film of water (including
hydroxide (•OH) and hydrogen (•H) radicals, oxygen ion (O2-), aqueous electron (eaq), hydrogen
peroxide (H2O2), hydrogen gas (H2), and the secondary radiolysis product, oxygen (O2)) that may
increase the waste form degradation rate and change radionuclide behavior.
2.1 Objective
The radiolysis model developed for this analysis is formulated as a set of coupled kinetics
equations for the reactions of aqueous species assumed to exist in the environment inside the
Engineered Barrier System (EBS). Radiolytic species are generated at a rate that is based on the
dose rate induced by the radiation field. Subsequent reactions of the radiolytic species are then
computed based on the reaction kinetics. The model inputs are the reaction rate constants, the
temperature and dose rate, the radiolytic G-values, and the initial concentrations of species in the
system. The conditional G-value for H2O2 production, (Gi,cond), is provided to the MPM (see
equation 2.3).
2.2 Physical Model
It is well known that the radiation emitted by used fuel will produce radiolysis products in the
presence of water vapor or a thin-film of water (including OH• and H• radicals, O2, eaq, H2O2,
H2, and O2). However, for these products to increase or change the rate of UNF degradation and
result in the release of radionuclides requires understanding the processes that might occur in
these interfacial regions.
The initial attempts of radiolysis model development concerned the production of radiolytic
species with time. Developing codes that would provide values for time periods relevant to
experimentation required modifying codes for stability. Diffusional terms were added to provide
greater realism in the model. This enabled determination of a ‘steady state’ value for a particular
radiolytic species or other chemical species distant from the fuel surface. These are the values
that would be provided to the MPM. A further improvement to the model has been to capture
the dose dependent radiolytic processes that would occur very close to the surface. This
adaptation has made the RM more closely related to the MPM. The earlier versions assumed
almost constant dose within the first 30 m of the surface where most alpha energy would be
deposited. However, it was realized that this was a poor representation of the system and this
region was further sub-divided into zones where the dose was modeled to change with distance
from the surface. The radiolysis model remains effectively a one-dimensional model of the
surface of the fuel.
Used Fuel Degradation: Experimental and Modeling Report 20 October 2013
Figure 2.1. Radiolysis model showing generation modified with a dose dependence term in the
irradiated zone and the diffusion zones across spatial regions.
The early versions of the radiolysis model were verified by using the reactions reported by
Pastina and LaVerne (2001) and those of Poinssot et al. (2005) to reproduce their results, which
had been done using FACSIMILE and MAKSIMA-CHEMIST kinetic software products,
respectively.
Table 2.1 Alpha particle G-values (Pastina and LaVerne, 2001)
Species G-value at 5 MeV
(molecules/100-eV)
H+ 0.18
H2O -2.58
H2O2 1.00
e(aq)− 0.15
•H 0.10
•OH 0.35
•HO2 0.10
H2 1.20
Used Fuel Degradation: Experimental and Modeling Report October 2013 21
User-defined inputs
Length of model diffusion grid (fuel surface to environmental boundary, default is 5
millimeters)
Number of calculation nodes (points) in diffusion grid (default is 24 ) with 14 zones in
the alpha penetration zone.
Duration of simulation (days to reach steady state)
Parameters
Alpha-particle penetration depth (35 µm)
Generation value for H2O2 (GH2O2) (moles per alpha energy deposited per time) (see
Table 2.1 for H2O2 and other species)
Rate constants (function of temperature) (taken from Pastina and LaVerne, 2001;
Poinssot et al. 2005)
Diffusion coefficients (function of temperature) (see Table 2.2)
Activation energies for temperature dependencies (available for H2O2 only)
Constants (not explicit in model)
pH of bulk solution (case dependent)
Pressure (O2, H2 are set and tracked as dissolved concentrations)
Variables
Dose rate
Temperature
Starting concentrations of oxidants and complexants: [O2], [CO32-
], [H2]
Calculated by model (output)
Conditional G-value for H2O2
Conditional G-values for all other species (not used in MPM)
2.3 Mathematical model
Concentrations in each region are coupled through diffusive currents and are expressed in
Equations 2.1 and 2.2. The coupled kinetics rate equations for the solution species
concentrations [Ai] are:
(2.1)
with rate constants kir, dose rate and radiolytic generation constants Gi, where the diffusive
currents (J (i)
) and diffusion constants (Di) appear in the discretized Fick’s Law according to:
Used Fuel Degradation: Experimental and Modeling Report 22 October 2013
(2.2)
for each component i in region n. Table 2.2 shows the values of diffusion constants used in the
model. For brevity, the “sum-of-products” on right-hand side of Equation 2.1 expresses the sum
of the product of reactant concentrations entering with reaction order Ojr where the
multiplication-index jr is over the nr reactants for reaction r. The notation includes the final state
order of component i produced by writing the rate constants kir, dependent on index i, but of
course that dependence only amounts to an integer (which could be zero) multiplied by the
reaction rate constants.
Table 2.2 Diffusion constants (Christensen and Sunder, 1996)
Species Di (10−5
•cm2•s
−1)
e(aq)− 4.9
OH 2.3
O− 1.5
H2O2 1.9
O2 2.5
H2 6.0
Others 1.5
2.3.1 Geometric scale
The length of the logarithmic grid of the model diffusion cell is adjustable but was set at 3
millimeters for all of the sensitivity runs performed to date (Figure 2.2). The number of
calculation points along the diffusion grid can also be set by the user but has been adjusted to
match the MPM.
We consider only the α-induced G-values (Table 2.1) because the near-field dose at the fuel
surface is strongly dominated by α-dose for decay times greater than 30 years when the dose is
~160 rad/s for 50 GWd/MTU used nuclear fuel (Raduldescu, 2011). Consistent with α-decay
radiation, the dose rate is assumed to be nonzero only in the nearest 35 μm to the fuel surface.
Figure 2 shows the spatial regions modeled from near the fuel surface to the external solution
boundary considered to be at 3.5 mm. The products of G-values with the dose rate act as
generation term to the kinetics equations for each of the species and are represented in Figure
2.2. Concentrations in each region are coupled through diffusive currents and are expressed in
Equations 2.1 and 2.2. Within the first 35 µm layer, the radiation dose will be greatest
immediately close to the fuel surface and then drop off. The radiolysis model can either consider
a constant average dose in this region, or consider the dose dependent production of radiolytic
species. In Figure 2.3, the effect of including or excluding dose dependence is shown.
Used Fuel Degradation: Experimental and Modeling Report October 2013 23
When the dose dependence is included, H2O2 production close to the fuel surface decreases. The
conditional G-value (Gi,cond), is calculated from Equation 2.3 (see below) for each node within
the alpha penetration zone :
(2.3)
where ρ is the density, ḋ, is the dose rate, and xd is the radiation zone distance.
Figure 2.2. Predicted conditional G-values for H2O2 with distance from the fuel surface showing
effect of external O2 at a fixed H2 concentration.
2.3.2 Time scale
The magnitude of each time step is determined by the total simulation time and the number of
temporal calculation points specified. Both of these values are set by the user. The time steps
are spaced logarithmically, with the finer spacing at the beginning of the run. For simulation
runs of 1-10 days, optimal time steps range from 0.1 seconds early in the simulation to hours
towards the end of the simulation.
The kinetics equations become unceasingly stiff as a dose rate of 137~rad/s is approached from
below (Figure 2.4). At a dose rate of 138 rad/s, the solution transitions to a new steady state
which is smaller in the H2O2 and O2 concentrations - even though the dose rate is greater. The
steady state solution is non-unique for this system. This is not surprising because of the many
non-linear terms in the kinetics equations. Additionally, at least two steady state solutions exist
above and below the critical dose rate, but only one is attained for a specific initial condition.
The dashed curves in Figure 2.5 assume that the dose rate changes continuously after the
previous steady state is attained in both the forward (red-dashed) and reverse (black-dashed)
Used Fuel Degradation: Experimental and Modeling Report 24 October 2013
direction. The dose change in the reverse (black-dashed) direction shows that two steady state
solutions exist even below the critical dose rate.
Figure 2.3. Time dependent concentration of H2O2 and O2 at the surface with dose rates of 40
rad/s (black), 80 rad/s (blue), 137 rad/s (red), 138 rad/s (green).
Figure 2.4. Steady-state concentrations of H2O2 at surface with dose rate for fixed initial
conditions (black-solid), forward running steady-stated (red-dashed), reverse running steady-
state (black-dashed).
Results from the radiolysis model including diffusional terms, suggests that steady state
conditions under two conditions can lead to discrete jumps in concentrations. It has been
observed, even at fixed dose rate that jumps in conditional G-values can occur.
Used Fuel Degradation: Experimental and Modeling Report October 2013 25
3. SUMMARY OF MIXED POTENTIAL MODEL
3.1 Objective and Background
The objective of the mixed potential model (MPM) is to calculate the used fuel degradation rates
for a wide range of disposal environments to provide the source term radionuclide release rates
for generic repository concepts. The fuel degradation rate is calculated for chemical and
oxidative dissolution mechanisms using mixed potential theory to account for all relevant redox
reactions at the fuel surface, including those involving oxidants produced by solution radiolysis.
The MPM was developed to account for the following key phenomena (Jerden et al. 2013):
Rate of oxidative dissolution of the fuel matrix as determined by interfacial redox
reaction kinetics (quantified as corrosion potential) occurring at the multiphase fuel
surface (phases include UO2 and the fission product alloy or epsilon phase).
Chemical or solubility based dissolution of the fuel matrix.
Complexation of dissolved uranium by carbonate near the fuel surface and in the bulk
solution.
Production of hydrogen peroxide (the dominant fuel oxidant in anoxic repository
environments) by alpha-radiolysis.
Diffusion of reactants and products in the groundwater away from and towards the
reacting fuel surface.
Precipitation and dissolution of a U–bearing corrosion product layer on the fuel surface.
Diffusion of reactants and products through the porous and tortuous corrosion layer
covering the reacting fuel surface.
Arrhenius-type temperature dependence for all interfacial and bulk reactions.
Because the MPM is based on fundamental chemical and electrochemical principles, it is flexible
enough to be applied to the full range of repository environments as well as shorter-term storage
scenarios being considered as part of the UFD campaign. The Argonne Mixed Potential Model
(MPM) was produced by implementing the Canadian mixed potential model for UO2 fuel
dissolution (King and Kolar, 1999, King and Kolar, 2003, Shoesmith et.al., 2003) using the
numerical computing environment and programming language MATLAB. The implementation
and testing of the Argonne MPM is discussed in the following reports: Jerden et al., 2012,
FCRD-UFD-2012-000169 and Jerden et al., 2013 FCRD-UFD-2013-000057 and the integration
of the MPM and RM with other process models being developed as part of the UFD program
was discussed in Sassani et al., 2012, M2FT-12SN0806062. The MPM includes a simplified
module for calculating the production of H2O2, which is the sole radiolytic species required in
the current implementation for granitic environments. This is being replaced by the RM to take
into account local variations in the concentrations of radiolytic species as affected by dose,
chemical interactions in the groundwater, decay, and diffusion. Key aspects of the MPM
affecting the integration of the RM, including the geometric and temporal scales of the models,
are discussed below.
Used Fuel Degradation: Experimental and Modeling Report 26 October 2013
3.2 Physical model
The MPM consists of ten one-dimensional reaction-diffusion equations (see Jerden et al., 2013),
that describe the mass transport, precipitation/dissolution and redox processes of the ten
chemical species included in the model. Figure 3.1 shows the MPM spatial diffusion grid and
the distribution of individual calculation nodes (shown as vertical lines).
Figure 3.1. Spatial diffusion grid for MPM showing individual calculation nodes as vertical lines
and summarizing key processes accounted for by the model (top image). Note the logarithmic
distribution of calculation points at the fuel/solution interface. The baseline number of
individual calculation nodes for the MPM is 200 (not all shown); however, this number can be
increased by the modeler if higher spatial resolution is required. The bottom image focuses on
how the presence of a U(VI) corrosion layer can influence the fuel degradation rate by blocking
alpha energy from being deposited in solution and by moderating the diffusion of species
towards and away from the reacting fuel surface.
Electrochemical rate expressions are used as boundary conditions for species that participate in
the interfacial electrochemical reactions. These reactions, as well as key bulk reactions
accounted for in the model are listed in Table 3.1.
Used Fuel Degradation: Experimental and Modeling Report October 2013 27
Table 3.1. Surface electrochemical reactions and bulk solution reactions tracked in the MPM.
Reactions
Anodic reactions at fuel surface
UO2 → UO22+
+ 2e-
UO2 + 2CO32-
→ UO2(CO3)22-
+ 2e-
H2O2 → O2 + 2H+ + 2e
-
H2 → 2H+ + 2e
-
Cathodic reactions at fuel surface
H2O2 + 2e- → 2OH
-
O2 + 2H2O + 4e- → 4OH
-
Homogeneous Bulk Reactions
UO22+
+ 2H2O → UO3:2H2O + 2H+
UO2(CO3)22-
+ 2H2O → UO3:H2O + 2CO32-
+ 2H+
UO3:H2O + 2CO32-
+ 2H+ → UO2(CO3)2
2- + 2H2O
O2 + 2H2O + 4Fe2+
→ 4Fe(III) + 4OH-
H2O2 + 2Fe2+
→ 2Fe(III) + 2OH-
UO22+
+ Fe2+
→ Fe(III) + U(IV)
UO2(CO3)22-
+ Fe2+
→ Fe(III) + U(IV) + 2CO32-
H2O2 → H2O + 0.5O2
The inclusion of alpha radiolysis in the MPM is essential because, at low concentrations of
dissolved oxygen, the only oxidants within a repository system are radiolytic species (e.g.,
molecular hydrogen peroxide). Therefore, predicting an accurate rate of fuel matrix degradation
in anoxic settings such as crystalline rock and clay/shale repository environments requires an
accurate description of radiolysis.
Calculating the alpha dose rate (and thus H2O2 concentration) for corroding UO2 fuel is
complicated by the effects of U(VI) corrosion products (modeled as schoepite, UO3•2H2O in
MPM). The U(VI) corrosion product layer has three effects on the rate of fuel degradation
predicted by the MPM:
Slows rate of oxidative dissolution by decreasing the reactive surface area of the fuel
(blocking or masking reaction sites).
Used Fuel Degradation: Experimental and Modeling Report 28 October 2013
Slows rate of oxidative dissolution by blocking alpha-particles from interacting with
water and producing radiolytic oxidants (decreases total moles H2O2 produced near fuel
surface). The magnitude of this effect is proportional to surface coverage of corrosion
layer.
Corrosion layer can slow the rate of oxidative dissolution by slowing the rate of diffusion
of oxidants to the fuel surface: U(VI) layer is a tortuous porous mass of crystals
(simulated in MPM by a parallel pores with constant tortuosity).
All three of these effects are modeled in the MPM by a radiolysis "sub-routine" that was recoded
(for details see Jerden et al., 2013) from the original Canadian mixed potential model (King and
Kolar, 1999). As in Canadian model, alpha-particles in the MPM are assumed to have a constant
energy of 5.3 MeV and a solution penetration distance (PEN) of 35 µm. The modeler can set the
penetration distance over the range of PEN = 45 micrometers for ~6.0 MeV alpha-particles down
to PEN = 10 m for ~2.3 MeV particles (King and Kolar, 1999). In the MPM, the default
generation value for hydrogen peroxide produced by alpha-radiolysis is assumed to be 1.021E-4
mol/Gy/m3 (Christensen and Sunder, 2000).
As stated above, the main objective of the current report is to present a strategy by which this
simplified radiolysis “sub-routine” can be replaced by the more rigorous radiolysis model. To
facilitate the discussion of this model integration effort, the geometry assumed for the MPM and
the chemical processes that are taken into account are summarized below:
User-defined inputs
Length of model diffusion grid (fuel surface to environmental boundary, default is 5
millimeters)
Number of calculation nodes (points) in diffusion grid (default is 200)
Duration of simulation
Surface coverage of fission product alloy phase
Parameters
Alpha-particle penetration depth
Generation value for H2O2 (GH2O2) (moles per alpha energy deposited per time). This will
be replaced by the Gi,cond which is calculated and passed from the RM to the MPM
(defined in section 2.3 above).
Charge transfer coefficients
Rate constants (function of temperature)
Standard potentials (function of temperature)
Diffusion coefficients (function of temperature)
Saturation con. U(VI) (function of temperature)
Activation energies for temperature dependencies
Porosity of schoepite (corrosion) layer
Used Fuel Degradation: Experimental and Modeling Report October 2013 29
Tortuosity of schoepite (corrosion) layer
Resistance between UO2 and fission product alloy (epsilon) phase
Constants (not explicit in model)
pH of bulk solution nominally 9.5 (pH implicit in parameter values)
Pressure (O2, H2 are set and tracked as dissolved concentrations)
Variables
Dose rate
Temperature
Starting concentrations of oxidants and complexants: [O2], [CO32-
], [H2], [Fe2+
]
Parameters Calculated by model (output)
Corrosion potential
Current densities for interfacial redox reactions
Flux of species from fuel surface
Concentrations of all species at each node (point) in diffusion grid after each time step
Corrosion layer thickness
3.3 Mathematical Model
The mathematical approach for the MPM is described in detail in Jerden et al., 2012 and Jerden
et al., 2013. The key aspects of the approach are how oxidants that cause fuel degradation are
treated. The two oxidants currently included in the MPM are (1) hydrogen peroxide, which is
formed by alpha radiolysis of water, and (2) oxygen, which has two sources: the initial amount in
the environment (set by modeler) and an amount formed by the decomposition of hydrogen
peroxide at the fuel surface and in the bulk solution. The mass balance equations that track
hydrogen peroxide and oxygen are shown as Equations 3.1 and 3.2 (applied at every node within
the 5 mm diffusion grid).
2 2
2+2 2
O O
f O 3 O Fe
C Cε = τ εD -εk C C
t x x
(3.1)
2 2 2 2
2+2 2 2 2 2 2
H O H O
f H O H O D 4 H O Fe
C Cε = τ εD +εG R -εk C C
t x x
(3.2)
where is the porosity of the schoepite corrosion layer (default value is 45%), Ci is concentration
of species i (moles/L), t is time (years), x is the horizontal distance along diffusion grid
(micrometers), is the tortuosity factor for pores in shoepite corrosion layer (default is 0.1), k3,
Used Fuel Degradation: Experimental and Modeling Report 30 October 2013
k4 are the rate constants for the reduction of oxygen and hydrogen peroxide by aqueous ferrous
iron by the reactions given in Equations (3.3) and (3.4), GH2O2 is the radiolytic generation value
of hydrogen peroxide (moles/(J/kg)/seconds), RD is dose rate (Gy/second). Similar mass balance
equations exist for all species included in the MPM.
O2 + H2O + 4Fe2+
→ 4 Fe3+
+ 4OH– (3.3)
H2O2 + 2Fe2+
→ 2Fe3+
+ 2OH– (3.4)
The thickness of the schoepite corrosion layer is determined by computing the integral of the
mass per volume (moles/m3) of schoepite for every grid point and using the molecular weight,
mineral density and porosity to determine the x dimension of the layer.
The rate of generation of hydrogen peroxide is determined by the generation factor in
mol/(J/kg)/m3 multiplied by the dose rate (J/kg) and the radiolysis cutoff distance [g(x)] which is
defined as the zone of solution irradiated by the fuel. In the current version of the MPM, the
amount of energy absorbed by solution in the 35 micrometer irradiated zone is constant. The
current model does not account for attenuation of the alpha particle energy away from the fuel
surface, but this may be included with the RM.
3.3.1 Geometric Scale
The length of the logarithmic grid of the model diffusion cell is adjustable but has been set at 5
millimeters (as shown in Figure 3.1) for all of the sensitivity runs performed to date. The number
of calculation points along the diffusion grid can also be set by the user. Based on the
simulations with times greater than 1000 years we have performed to-day, 200 grid points
provides a good balance between the amount of time required to run the model and the spatial
resolution of component concentrations within the grid.
3.3.2 Time Scale
The magnitude of each time step is determined by the total simulation time and the number of
temporal calculation points specified. Both of these values are set by the user. The time steps
are spaced logarithmically, with the finer spacing at the beginning of the run. For simulation
runs of 10000 years or more, optimal time steps range from 0.1 years early in the simulation to
1000 years towards the end of the simulation.
3.4 Example of MPM Calculations
Figure 3.2 shows examples of results from MPM simulations of reaction for ten thousand years
with hydrogen peroxide generation values from 1.0E-4 moles/(J/kg)/m3 (theoretical value from
Christensen and Sunder, 2000) to 1.0E-5 moles/(J/kg)/m3 (arbitrarily chosen to study model
sensitivity). For this model run the temperature and dose rate within the model diffusion grid
were held constant at 25oC and 0.1 Gy/s respectively, the initial oxygen concentration was 1.0E-
6 moles/L and the background concentrations of carbonate, iron and hydrogen were set to zero.
To give a sense of the temporal resolution of the model for the default settings of 200 grid points
and 100 time steps, results for each time step are shown as individual data points in Figure 3.2.
The top plot shows that the rate of oxidative dissolution of the fuel decreases by a factor of
Used Fuel Degradation: Experimental and Modeling Report October 2013 31
approximately 2 due to the precipitation of the schoepite corrosion layer, which physically
prevents alpha particles from irradiating the solution at the surface of the fuel. Because the
corrosion layer is modeled as a set of uniform parallel pores, the amount of fuel area masked is
determined by its porosity (default is 50%). The oxidative dissolution rate is also predicted to
decrease by a factor of 8 due to this lower production rate of hydrogen peroxide from the order
of magnitude decrease in the GH2O2. The dissolution rate does not decrease further because the
background concentration of oxygen supports oxidative dissolution of the fuel.
The middle diagram of Figure 3.2 shows the current densities for the dominant interfacial redox
reactions. The kinetic balance of these cathodic and anodic reactions determines the corrosion
potential from which the oxidative dissolution rate of the fuel is calculated. The bottom diagram
shows the steady state diffusion profiles for hydrogen peroxide over the diffusion grid. This plot
highlights the effect of the schoepite corrosion layer in both blocking alpha-particles emitted
from the fuel from irradiating the solution and in moderating the diffusion to and from the
reacting fuel surface.
Used Fuel Degradation: Experimental and Modeling Report 32 October 2013
Figure 3.2. Results from recent MPM runs investigating the sensitivity of fuel degradation rate to
changes in the G-value for H2O2 in mole/(J/kg)/second (top). Individual time steps are
represented as single data points. The middle diagram shows the reaction current densities
(GH2O2=1.0E-5) for the redox reactions that determine the fuel corrosion potential and fuel
degradation rate. The bottom diagram shows H2O2 concentration profiles for the two time steps
identified in the top diagram.
Used Fuel Degradation: Experimental and Modeling Report October 2013 33
4. COUPLING MPM/RM MODELS
Coupling the RM and MPM will provide a scientifically rigorous predictive tool for calculating
the degradation rate of used fuel. By combining the models, we ensure that the fuel degradation
calculations used to determine performance assessment source terms account for all major
radiolytic, electrochemical and corrosion processes that can influence radionuclide release. The
conceptual approach for coupling the RM and MPM is summarized in Figure 4.1. This diagram
shows that the integrated Fuel degradation model consists of three modules:
The Radiolysis Module (green box), which provides a rigorous treatment of chemical
processes associated with the absorption of ionizing radiation near the surface of the
exposed fuel. Supplies concentrations used to calculate fuel matrix degradation.
The Mixed Potential Module (blue process boxes), which provides the rate of fuel matrix
degradation (accounts for both oxidative and chemical dissolution).
The Instant Release Fraction, which provides the masses of key radionuclides that will
be released from the fuel promptly after the time of exposure (release rate is more rapid
than predicted matrix degradation rate).
Figure 4.1. Summary information flow diagram highlighting the coupling of radiolysis, matrix,
and instant release process modules within the FDM (MPM shown by blue boxes, RM by green
box, and IRF by red box), and PA.
The strategy for development and implementation of the integrated Fuel Degradation Model
(FDM) involves the flow of information both to and from other performance assessment level
models. As shown in Figure 4.1, required inputs to the FDM include quantitative descriptions of
the composition of the groundwater/in-package solution in contact with the fuel as well as
information regarding the fuel being modeled, such as the changes in fuel temperature and dose
rate with time. The temperature and dose information, which are directly used in the FDM, are
Used Fuel Degradation: Experimental and Modeling Report 34 October 2013
determined by the fuel burn-up as well as the decay or cooling time elapsed prior to fuel
exposure to environmental solutions (e.g., time before repository emplacement + time after
emplacement before waste package failure).
The initial conditions, temperature and dose rate functions will be combined with an extensive
radiolysis-electrochemical-kinetic database and used by the FDM to produce a rate of fuel matrix
degradation. The matrix degradation rate will be combined with inventory-specific instant
release fraction calculation to yield a radionuclide mobilization rate source term on a per waste
package basis for performance assessment calculations.
As shown in Figure 4.1, the key link between the RM and MPM is the conditional generation
values for radiolytic species. Conditional generation values take into account the effects of
shielding by alteration layers and chemical reactions in the evolving solution on the G values
(Gi,cond). Coupling of the models involves the passing of spatial solution concentrations from the
MPM to the RM and then the conditional generation values for relevant species from the RM to
the MPM for use in the next time step of the MPM (Figure 4.1). For this exchange to work, the
spatial calculation grid within the alpha penetration zone must be identical in each model
(currently 14 nodes within 35 micrometers of the alpha source).
4.1 Parameter values provided by RM to MPM
The RM will provide conditional G-values for all oxidants capable of degrading the fuel
(currently H2O2 and O2) as well as hydrogen, which can protect the fuel from oxidative
dissolution if its oxidation is catalyzed at the reacting surface. The conditional G-values will be
supplied to the MPM for every calculation node located within the α-particle penetration zone
(currently 14 nodes over the 35 µm α-particle penetration zone).
The conditional G-values calculated by the RM are more accurate that the theoretical GH2O2 used
as a default in the MPM because the RM accounts for the diffusion of, and reactions between,
intermediate radiolytic species such as eaq-,•H, •OH, •OH2, and •CO3
-. Examples of reactions
that can lead to a decreased yield of hydrogen peroxide relative to the amount predicted in the
MPM are:
H2O2 + eaq- → OH- + •OH (4.1)
H2O2 + •H → H2O + •OH (4.2)
H2O2 + •OH → H2O + •OH2 (4.3)
H2O2 + •OH2 → H2O + O2 + •OH (4.4)
H2O2 + •CO3- → CO3
2- + O2
- + 2H
+ (4.5)
4.2 Parameter values provided by MPM to RM
For the RM to calculate an accurate description of the generation values for relevant radiolytic
species (e.g., H2O2) it needs the following information from the MPM:
Concentrations of species that are radiolytically active (e.g., species such as CO32-
or Cl-
that produce reaction cascades when excited) or otherwise interact with radiolytic species
(e.g., O2, H2, FeII).
Used Fuel Degradation: Experimental and Modeling Report October 2013 35
The modified diffusion coefficients for all relevant species (e.g., O2, H2, FeII, CO3
2) at all
calculation nodes present within the tortuous corrosion layer (see Figure 2 for visual
explanation of assumed corrosion product geometry)
Matching/partitioning physical, chemical, radiolytic processes
Physical, chemical and radiolytic processes will matched by ensuring that the same spatial
diffusion grid is used for both models. Diffusion depends on the spatial dimension of the grid, so
a uniform 5 millimeter linear distance will be used for both models as a default; however, this
value can be altered by the modeler. To ensure that the chemical and radiolytic processes match
both models will contain the same number, and spacing of calculation nodes within the alpha
penetration zone (default is 14 nodes). The key time and space dependent variables dose rate
and temperature will also be matched in the two models.
Coordinating time scales
The RM calculations that produce the conditional G-values require short time steps relative to
the MPM (kinetics on order of seconds). Therefore, the two models will not be time
synchronized. Rather the RM will be run independently and the resulting conditional G-values
will be handed off at a specific time point during a MPM simulation. There are three options for
timing this hand-off:
Option: Use RM to provide conditional G–value at each time step in MPM
Option: Use RM to provide conditional G–value after a constant number of time steps in
MPM
Option: Use the RM to identify solution concentrations that have significant impact on
[H2O2] and conditional G-value
The best option in terms of model fidelity is for the RM to provide the conditional G-values at
the beginning of each MPM time step. This will be the option pursued as we move forward with
implementation of the coupled model.
Conditional G-factor
Gcond is defined as the steady state generation value (moles of species (i) per alpha energy
deposited) averaged over the 35 micrometer alpha penetration depth adjacent to the fuel surface.
The Gcond value is generated from Equation 2.3 for feeding into the MPM. The conditional G-
value is dependent on the solution conditions and environment.
To accurately calculate Gcond for a solution generated by a given number of MPM time steps, the
RM will need the following information:
Dose rate.
Temperature.
Concentrations of reactive species [O2], [H2], [CO32-
], and for application to other generic
forms of geologic repository, terms for [Cl-], [Br
-], [SO4
2-], and others will become
important.
Diffusion coefficients of relevant species at the last MPM step (these change in alpha
penetration zone when a corrosion layer is present due to tortuosity factor.)
Used Fuel Degradation: Experimental and Modeling Report 36 October 2013
Thickness of corrosion layer.
The dose rate and temperature are characteristics of the fuel and disposal system, and the other
values are calculated or tracked in MPM. All are handed off to RM whenever it is determined
that a new Gcond is needed for the next time step of the MPM run. The need for a new Gcond could
be triggered by concentration thresholds determined to result in significant changes in the G-
values from previous sensitivity runs (e.g., sets of H2 and O2 concentrations that favor the rapid
decomposition of H2O2) (see Figure 2.3 and 2.4).
4.3 Interface Approaches
Several options being considered for coupling the RM and MPM are listed below. Different
options have advantages and disadvantages based on the extent of coding that would be required
and the ease of use of the final product.
Option 1: Add radiolysis module as subroutine within mixed potential module code. This would
involve re-coding the RM from Fortran into MATLAB or alternatively recoding the MPM into
Fortran so that the two models would run as part of the same program.
Pros: full RM code included in integrated model, not limited to abstracted form of the
RM, seamless transfer of information.
Cons: relatively large amount of time and effort required to support recoding.
Option 2: Represent radiolysis module as an analytical expression within mixed potential
module code. This would involve minimal coding in MATLAB, but would require significant
effort to define an analytical form that captures the full range of conditional dependencies
accounted for in the RM.
Pros: coding work is streamlined and simplified, seamless transfer of information.
Cons: uncertainty of success of approach, it is not clear that a single analytical expression
can capture all of the relevant conditional dependencies accounted for in the full RM.
Option 3: Provide radiolysis module results as look-up table of conditional generation values
produced by running the RM over the full range of relevant conditions. This G-value look-up
table would be treated by the MPM as part of the parameter database.
Pros: no coding work needed, seamless transfer of information.
Cons: relatively large amount of time and effort to produce exhaustive table that
considers all relevant conditions,
Option 4: Maintain radiolysis model and mixed potential module as separate codes that call each
other during a fuel degradation model run.
Pros: no coding work needed, not limited to abstracted version of the RM.
Cons: uncertainty of success of approach, it is not clear that the Fortran and MATLAB
codes and pass the needed information back and forth as they currently exist. Even if
possible this approach may dramatically increase computing time needed to run the
FDM.
Used Fuel Degradation: Experimental and Modeling Report October 2013 37
4.3.1 Sensitivity Analysis: MPM (MATLAB) – DAKOTA Interfacing
4.3.1.1 Introduction
The source term is a very important element of repository performance assessment (PA) that
describes the spatio-temporal variations in radionuclide releases in a disposal environment.
Intrinsic geologic and geochemical complexities and their time-dependent interactions in the host
medium can produce a large suite of scenarios for radionuclide releases and migration in the
disposal environment. For this reason, uncertainty and sensitivity analyses are essential to the
evaluation of process models and their responses to the disposal concept PA (Helton et al., 2006;
Saltelli et al., 2000).
Sensitivity analysis (SA) methodologies are key to the evaluation of the simulation parametric
responses affecting model behavior and their uncertainties, particularly in complex systems. SA
permits the analysis of distinct input perturbations and their influence to model outputs where
various approaches have been applied to a wide variety of process models, including those
relevant to chemical systems (Helton et al., 2006; Saltelli, 2009; Saltelli et al., 2005, 2012;
Saltelli et al., 2000; Saltelli et al., 2004). Saltelli et al. (2000) provides an example of the
application of SA methods to the analysis of radionuclide migration in natural and engineered
barriers on the basis of chemical mass transfer and reaction in a porous medium. Given the
emphasized importance of SA to PA and also to model integration and analysis, SA of the used
fuel corrosion model has been conducted based on variations of key environmental inputs. The
next sections describe the approach entailing code coupling of the ANL Mixed Potential Model
and the DAKOTA code suite for uncertainty quantification and optimization.
4.3.1.2 Sensitivity Analysis (SA): Approach Description
Sensitivity analyses of the Mixed Potential Model (MPM) were conducted by externally-
coupling the MPM Matlab code with the DAKOTA toolkit in a Microsoft Windows 7
environment. DAKOTA is an open source multilevel parallel object-oriented framework
developed at Sandia National Laboratories. The DAKOTA code suite contains a large collection
of algorithms to conduct optimization, uncertainty quantification (UQ), and sensitivity analysis.
The external coupling uses shell scripting commands to post-process MPM output responses that
are input to DAKOTA. Figure 4.2 shows a generalized schematic diagram showing the
information flow in the MPM-DAKOTA coupling.
Figure 4.2. Schematic diagram depicting the information flow for the MPM (Matlab) –
DAKOTA coupling.
Mixed Potential Model (MPM)
(MATLAB)
DAKOTAResults File
(post-processing)
MPM Output File
DAKOTASensitivity Analysis
Full Factorial
DAKOTAParameters File(pre-processing)
MPM Input File
Used Fuel Degradation: Experimental and Modeling Report 38 October 2013
The analysis was done using the multidimensional parameter (full-factorial) evaluation in
DAKOTA where each input variable is partitioned in equally-spaced intervals for their
continuous value ranges within their upper and lower bounds. The number of partitions is set to
generate four data points (four DAKOTA-MPM iterations) for each input value. The MPM
model inputs to be perturbed at each DAKOTA-MPM iteration are temperature, dose rate, and
initial CO3--
and O2 concentrations. This partitioning coverage equals to four input evaluations
for each of the four input parameters resulting in 44 or 256 DAKOTA-MPM iteration runs. The
output responses to be sampled are the concentrations UO2++
, UCO3--, and H2O2. The UO2
++ and
UCO3--
are considered as the total concentration of U released into the system. The bounds for
the input variables (Table 4.1) were based on reasonable ranges of possible geochemical
conditions in the disposal gallery and fuel surface but spaced a few orders of magnitude to
capture a wide series of values. The sampled output responses are taken at 1097 years and at a
surface distance of 31.6 microns. It should be noted that other sampled times and surface
distances can be considered in the response sampling in the SA. The effect of considering
uncertainties and other sampling strategies for the considered input factors was not evaluated in
this SA and it may well be a topic of future work.
Table 4.1. Bounding constrains for input variables for DAKOTA.
Constraint*
Temperature
(K)
Dose Rate
(J/kg)/s
[CO3--]
(moles/m3)
[O2]
(moles/m3)
Lower Bounds 298.15 0.001 0.01 1.0E-05
Upper Bounds 363.15 0.5 1.5 1.0E-02
* Partitioning between these bounding limits was set to produce four data points. For example, the resulting
temperature values for this bounded range are 298.15, 319.8, 341.5, and 363.15 K.
Used Fuel Degradation: Experimental and Modeling Report October 2013 39
Table 4.2. Simple DAKOTA Correlation Matrix among all inputs and outputs
Inputs/Outputs Temperature
(K)
Dose Rate
((J/kg)/s)
[CO3--]
(mol/m3)
[O2]
(mol/m3)
[UO2++
]
(mol/m3)
[UCO3--]
(mol/m3)
[H2O2]
(mol/m3)
Temperature
(K) 1.00E+00 - - - - - -
Dose Rate
((J/kg)/s) 0.00E+00 1.00E+00 - - - - -
[CO3--]
(mol/m3)
-4.24E-22 0.00E+00 1.00E+00 - - - -
[O2]
(mol/m3)
0.00E+00 8.47E-22 8.47E-21 1.00E+00 - - -
[UO2++
]
(mol/m3)
6.79E-01 5.13E-01 -4.81E-02 3.57E-01 1.00E+00 - -
[UCO3--]
(mol/m3)
-6.39E-01 3.23E-01 3.23E-01 8.01E-02 -3.75E-01 1.00E+00 -
[H2O2]
(mol/m3)
-5.64E-01 6.56E-01 -4.37E-02 1.67E-02 -1.20E-01 7.16E-01 1.00E+00
4.4 Discussion and Future Work
DAKOTA provide a matrix table of the outputs (256 MPM code runs) for all the sampled
iterations. It also provides a simple correlation matrix given in Table 4.2. This correlation
matrix is useful in delineating the parameter sensitivities to the input factors. Figures 4.3 and 4.4
show the resulting total U and H2O2 concentrations profiles as a function of temperature for the
lower and upper bounds of initial CO3-- and O2 concentrations at the specified dose rates. Note
that the main influence in U and H2O2 concentration profiles is the dose rate. For example, U
and H2O2 concentrations are increased by about the same order of magnitude as the dose rate for
the same initial CO3-- and O2 concentrations. The effects from the latter two have some
influence, particularly O2 concentration, but not as large as the dose rate. These observations
lead to the conclusion that dose rates from radiolysis need to be closely integrated with the H2O2
production rates which in turn determines the U releases. However, conditions at the fuel
surface and surrounding are expected to be largely reduced and the SA should consider lower O2
concentrations. Still, the relative magnitude of the effect of CO3-- and O2 concentrations is not
expected to greatly surpass that of the dose rate. The figures also show an overlapping band of
the U and H2O2 concentration profiles at dose rates within approximately less than an order of
magnitude for dose rates ranging from 0.167 to 0.5 (J/kg)/s.
Used Fuel Degradation: Experimental and Modeling Report 40 October 2013
This type of analysis is very useful in investigating model sensitivities but it can also be utilized
for model verification and testing. Further, it provides the groundwork for expanding the
analysis with other SA strategies towards the analysis of model uncertainties. The coupling of
the MPM with the DAKOTA toolkit offers access to a large set of tools for optimization (e.g.,
regression analysis) and uncertainty quantification. For FY14, the analysis will be expanded to:
Evaluate sampling strategies (e.g., Latin Hypercube Sampling or LHS) other than
bounding constrains as done in a full-factorial design,
Consider time dependencies in key variables to used fuel degradation such as radiolytic
processes,
Examine model responses to specific host media aqueous chemistry and related input
uncertainties.
Figure 4.3. Concentration profile of U aqueous species computed by the MPM as a function of
temperature, dose rate, CO3--, and O2 concentrations.
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
295 305 315 325 335 345 355 365 375
[UO
2+
+ ] +
[U
CO
3--]
(mo
l/m
3)
T(K)
Dose Rate = 0.001 (J/kg)/s Dose Rate = 0.167 (J/kg)/s
Dose Rate = 0.33 (J/kg)/s Dose Rate = 0.5 (J/kg)/s
Dose Rate = 0.001 (J/kg)/s Dose Rate = 0.167 (J/kg)/s
Dose Rate = 0.33 (J/kg)/s Dose Rate = 0.5 (J/kg)/s
[CO 3--] = 1.0 mol/m3
[O2] = 1.0E-02 mol/m 3
[CO 3--] = 0.01 mol/m3
[O2] = 1.0E-05 mol/m 3
Used Fuel Degradation: Experimental and Modeling Report October 2013 41
Figure 4.4. Concentration profile of H2O2 computed by the MPM as a function of temperature,
dose rate, CO3--, and O2 concentrations.
5. CONCLUSIONS
The Gcond is calculated in the RM and handed off to the MPM, where it is used to calculate the
spatial generation of [H2O2] from the dose rate as affected by surface reactions with the fuel and
diffusion. Gcond is defined as the steady state generation value (moles of species (i) per alpha
energy deposited) averaged over the 35 µm alpha penetration depth adjacent to the fuel surface.
It is useful though not entirely necessary that the total deposition depths are the same in the RM
and MPM, and it may be valuable that they be discretized the same. This is because the H2O2
concentration is calculated at much shorter time scales within the RM compared to the MPM.
When using the discretized case of the RM, Gcond becomes proportional to the diffusive flux of
species (i) exiting the alpha penetration zone.
The coupling of the RM and MPM requires running the models separately because the MPM
uses time steps on the order of years, while the RM uses time steps on the order of seconds. An
alternative to actively linking the RM and MPM is to develop an analytic expression that
determines Gcond for a given set of conditions. The analytic expression would be coded directly
into MATLAB and run with the MPM. However, this does not establish a true working link and
the full capabilities of RM would be lost. Furthermore, the determination of analytical
expressions for the full ranges of environments may prove to be onerous.
Interfacing of the MPM with the DAKOTA code suite has been developed to conduct sensitivity
analyses. The results of this analysis provide the necessary tools to feasibly evaluate model
behavior in response to the variability of multiple parameters which is important to the
determination of PA inputs. Such interfacing also provides a fertile ground to expand SA to
other parameters and to conduct uncertainty quantification or parameter optimization if
Dose Rate = 0.001 (J/kg)/s Dose Rate = 0.167 (J/kg)/s
Dose Rate = 0.33 (J/kg)/s Dose Rate = 0.5 (J/kg)/s
Dose Rate = 0.001 (J/kg)/s Dose Rate = 0.167 (J/kg)/s
Dose Rate = 0.33 (J/kg)/s Dose Rate = 0.5 (J/kg)/s
[CO3
--] = 1.0 mol/m 3
[O2] = 1.0E-02 mol/m3
[CO3
--] = 0.01 mol/m3
[O2] = 1.0E-05 mol/m 3
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
295 305 315 325 335 345 355 365 375
T(K)
[H2O
2]
(mo
l/m
3)
Used Fuel Degradation: Experimental and Modeling Report 42 October 2013
necessary. Future work includes the consideration of other sampling strategies and the analysis
of time dependencies (e.g., how a precipitating solid affects U concentration files with time).
Currently the only radiolytic species in the MPM is H2O2. Other radiolytic species will need to
be added to the MPM for it to be applicable to the full range of relevant geologic and EBS
environments. The radiolytic species that need to be added can be determined by sensitivity runs
using the RM for the range of relevant solution compositions for sites of interest. The focus of
RM sensitivity runs should be on radiolytically active species (for example: Cl-, Br
-, NO3
-, CO3
2-,
SO42-
) and should determine concentration thresholds above which radiolytic species other than
H2O2 significantly impact fuel oxidation become important.
Used Fuel Degradation: Experimental and Modeling Report October 2013 43
6. REFERENCES (Sections 1 through 5)
BSC (2004). CSNF Waste Form Degradation: Summary Abstraction, ANL-EBS-MD-000015
REV02.
Christensen, H., Sunder, S. (1996). An evaluation of water layer thickness effective in oxidation
of UO2 fuel due to radiolysis of water, Journal of Nuclear Materials 238: 70-77.
Christensen, H., Sunder. S. (2000). Current state of knowledge of water radiolysis effects on
spent nuclear fuel corrosion, Nuclear Technology, 131, p. 102-123.
Clayton D., Freeze, G., Hadgu, T., Hardin, E., Lee, J., Prouty, J., Rogers, R., Nutt, W. M.,
Birkholzer, J., Liu, H.H., Zheng, L., and Chu, S. (2011). Generic Disposal System
Modeling—Fiscal Year 2011 Progress Report, FCRD-USED-2011-000184, pp. 443.
Cunnane, J.C., Fortner, J.A, and Finch, R. (2003). The behavior of light water reactor fuel after
the cladding is breached under unsaturated test conditions, MRS Symposium
Proceedings,757, p. 385–392.
De Pablo, J., Serrano-Purroy, D., Gonzalez-Robles, E., Clarens, F., Martinez-Esparza, A.,
Wegen, D. H., Casas, I., Christiansen, B., Glatz, J.-P., Gimenez, J. (2009). Effect of HBS
Structure in Fast Release Fraction of 48 GWd/tU PWR Fuel, Mater. Res. Soc. Symp. Proc.,
1193, 613 doi:10.1557/PROC1193613.
Ferry, C., Poinssot, C., Cappelaere, C., Desgranges, L., Jégou, C., Miserque, F., Piron, J.P.,
Roudil, and D., Gras, J-M. (2006). Specific Outcomes of the Research on the Spent Fuel
Long-Term Evolution in Interim Dry Storage and Deep Geological Disposal, Journal of
Nuclear Materials, 352, p. 246-253.
Freeze, G., Mariner, P., Houseworth, J., Cunnane, J., and F. Caporuscio, F. (2010). Used Fuel
Disposition Campaign Features, Events, and Processes (FEPs): FY10 Progress Report,
August 2010.
Freeze, G. and Vaughn, P. (2012). Performance Assessment Framework Requirements for
Advanced Disposal System Modeling, FCRD-UFD-2012-000227 (M3FT-12SN0808062),
U.S. Department of Energy, Office of Nuclear Energy, Used Fuel Disposition Campaign,
Washington, D.C.
Freeze, G., Gardner, P., Vaughn, P., Sevougian, S. D., Mariner, P., Mousseau, V. (2013).
Performance Assessment Modeling of a Generic Salt Disposal System: Annotated Outline,
DOE-NE Fuel Cycle R&D, FCRD-UFD-2013-000219, SAND2013-6183P, 21 pp.
Helton, J. C., Johnson, J. D., Sallaberry, C. J., and Storlie, C. B. (2006). Survey of sampling-
based methods for uncertainty and sensitivity analysis: Reliability Engineering and System
Safety, v. 91, no. 10, p. 1175-1209.
Helton, J. C., Johnson, J. D., Sallaberry, C. J., and Storlie, C. B. (2006). Survey of sampling-
based methods for uncertainty and sensitivity analysis: Reliability Engineering and System
Safety, v. 91, no. 10, p. 1175-1209.
Jerden, J., Frey, K., Cruse, T., and Ebert, W. (2012). Waste Form Degradation Model Status
Report: Electrochemical Model for Used Fuel Matrix Degradation Rate. FCRD-UFD-
2012-000169.
Used Fuel Degradation: Experimental and Modeling Report 44 October 2013
Jerden, J., Frey, K., Cruse, T., and Ebert, W. (2013). Waste Form Degradation Model Status
Report: ANL Mixed Potential Model, Version 1. Archive. FCRD-UFD-2013-000057.
Johnson, L., Ferry, C., Poinssot, C., and Lovera, P. (2005). Spent fuel radionuclide source term
model for assessing spent fuel performance in geological disposal. Part I: Assessment of
the Instant Release Fraction, Journal of Nuclear Materials, 346, p. 66-77.
Johnson, L., Gunther-Leopold, I., Kobler Waldis, J., Linder, H. P., Low, J., Cui, D., Ekeroth, E.
Spahiu, K., Evins, L. Z. (2012). Rapid aqueous release of fission products from high burn-
up LWR fuel: Experimental results and correlations with fission gas release, Journal of
Nuclear Materials, 420, p. 54-62.
Jové Colón, C. F., Greathouse, J. A., Teich-McGoldrick, S., Cygan, R. T., Hadgu, T., Bean, J. E.,
Martinez, M. J., Hopkins, P. L., Argüello, J. G., Hansen, F. D., Caporuscio, F. A.,
Cheshire, M., Levy, S. S., McCarney, M. K., Greenberg, H. R., Wolery, T. J., Sutton, M.,
Rutqvist, J., Steefel, C. I., Birkholzer, J., Liu, H. H., Davis, J. A., Tinnacher, R., Bourg, I.,
Holmboe, M., and Galindez, J. (2012). Evaluation of Generic EBS Design Concepts and
Process Models: Implications to EBS Design Optimization, SAND2012-5083 P, 250 pp.
King, F. and Kolar, M. (1999). Mathematical Implementation of the Mixed-Potential Model of
Fuel Dissolution Model Version MPM-V1.0, Ontario Hydro, Nuclear Waste Management
Division Report No. 06819-REP-01200-10005 R00.
King, F. and Kolar, M. (2002). Validation of the Mixed-Potential Model for Used Fuel
Dissolution Against Experimental Data, Ontario Hydro, Nuclear Waste Management
Division Report No. 06819-REP-01200-10077-R00.
King, F. and Kolar, M. (2003). The Mixed-Potential Model for UO2 Dissolution MPM Versions
V1.3 and V1.4, Ontario Hydro, Nuclear Waste Management Division Report No. 06819-
REP-01200-10104 R00.
Pastina, B. and LaVerne, J. A. (2001). Effect of Molecular Hydrogen on Hydrogen Peroxide in
Water Radiolysis, Journal of Physical Chemistry A105: 9316-9322.
Poinssot, C. Ferry, C. M. Kelm, B. Grambow, A. Martinez, A., Johnson, L., Andriamoloolona,
Z., Bruno, J., Cachoir, C., Cavedon, J.M., Christensen, H., Corbel, C., Jegou, C., Lemmens,
K., Loida, A., Lovera, P., Miserque, F. de Pablo, J., Poulesquen, A., Quinones, J.
Rondinella, V., Spahiu, K., and D. H. Wegen, (2004). Spent Fuel Stability under
Repository Conditions: Final Report of the European Project, European Commission, 5th
EURATOM FRAMEWORK PROGRAMME, 1998-2002.
Poinssot, C., Ferry, C., Lovera, P., Jégou, C., Gras, J-M. (2005). Spent fuel radionuclide source
term model for assessing spent fuel performance in geological disposal. Part II: Matrix
alteration model and global performance, Journal of Nuclear Materials, 346, p. 66-77.
Radulescu, G. (2011). Radiation Transport Evaluations for Repository Science, ORNL/LTR-
2011/294, LETTER REPORT, Oak Ridge National Laboratory, August, 2011.
Roudil, D., Jegou, C., Broudic, V. Muzeau, B., Peuget, S., and Deschanels, X. (2007). Gap and
grain boundaries inventories from pressurized water reactor spent fuels, Journal of Nuclear
Materials, 362, p. 411-415.
Used Fuel Degradation: Experimental and Modeling Report October 2013 45
Sassani, D.C., Jové Colón, J. C., Weck, P., Jerden, J. L., Jr., Frey, K. E., Cruse, T., Ebert, W. L.,
Buck, E. C., Wittman, R. S., Skomurski, F. N., Cantrell, K. J., McNamara, B. K., and
Soderquist, C. Z. (2012). Integration of EBS Models with Generic Disposal System Models,
U.S. Department of Energy, Used Fuel Disposition Campaign milestone report: M2FT-
12SN0806062, September, 7 2012
Sassani, D. C., Jové-Colón, C. F., and Weck, P. F. (2013). “Integrating Used Fuel Degradation
Models into Generic Performance Assessment” for the ANS 2013 International High-level
Radioactive Waste Management Conference, April 28 – May 3, 2013, Albuquerque, NM.
Saltelli, A. (2009). Special issue: Sensitivity Analysis: Reliability Engineering and System
Safety, v. 94, no. 7, p. 1133-1134.
Saltelli, A., Ratto, M., Tarantola, S., and Campolongo, F. (2005) Sensitivity analysis for
chemical models: Chemical Reviews, v. 105, no. 7, p. 2811-2827.
- (2012). Update 1 of: Sensitivity Analysis for Chemical Models: Chemical Reviews, v. 112, p.
Pr1-Pr21.
Saltelli, A., Tarantola, S., and Campolongo, F. (2000). Sensitivity analysis as an ingredient of
modeling: Statistical Science, v. 15, no. 4, p. 377-395.
Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M. (2004). Sensitivity analysis in practice:
a guide to assessing scientific models, John Wiley & Sons.
Serrano-Purroy, D., Clarens, F., Gonzalez-Robles, E., Glatz, J.-P., Wegen, D. H., De Pablo, J.,
Casas, I., Gimenez, J., Martinez-Esparza, A. (2012). Instant release fraction and matrix
release of high burn-up UO2 spent nuclear fuel: Effect of high burn-up structure and
leaching solution composition, Journal of Nuclear Materials, 427, p. 249-258.
Shoesmith, D.W., Kolar, M., and King, F. (2003). A Mixed-Potential Model to Predict Fuel
(Uranium Dioxide) Corrosion Within a Failed Nuclear Waste Container, Corrosion, 59,
802-816.
Une, K., Kashibe, S., 1996, Corrosion behavior of irradiated oxide fuel pellets in high
temperature water, Journal of Nuclear Materials, 232, p. 240-247.
Weck, P. F., Kim, E., Jové Colón, C. F., and Sassani, D. C., 2013, On the role of strong electron
correlations in the surface properties and chemistry of uranium dioxide, DOI:
10.1039/C3DT32536A.
Wittman, R. S. and Buck, E. C. (2012). Sensitivity of UO2 stability in a reducing environment on
radiolysis model parameters, Materials Research Society Proceedings Symposium, 1444, 3-
8.
Yu, L., Weetjens, E., Vietor, T., and Hart, J. (2010). Integration of TIMODAZ within the safety
case and recommendations for repository design (D14), Final Report of WP6, European
Commission Euratom Research and Training Programme on Nuclear Energy, 48 pp.
Used Fuel Degradation: Experimental and Modeling Report 46 October 2013
7. ANL MIXED POTENTIAL MODEL WITH EXPERIMENTAL RESULTS: IMPLEMENTATION OF NOBLE METAL PARTICLE CATALYSIS MODULE
7.1 Objectives and Context
The high level goal of this work is to develop a fundamentals-based computational tool for
predicting the degradation rate of used fuel and establish a scientific basis for the radionuclide
source terms used in the UFD generic performance assessment model. The approach has been to
implement, optimize and extend an existing and well-tested corrosion model that is based on
electrochemical mixed potential theory (the Canadian mixed potential model - MPM) to specific
fuel degradation processes of interest and to couple this MPM with an equally robust radiolysis
model (RM) (for conceptual discussion of model coupling see Buck et al., 2013). The coupled
MPM – RM process model is being combined with a statistical treatment of radionuclide instant
release fractions (IRF) to form the Fuel Degradation Model (FDM). Thus, the FDM consists of
three primary components:
The Radiolysis Module (RM), which provides a rigorous treatment of chemical processes
associated with the absorption of ionizing radiation near the surface of the exposed fuel.
Supplies concentrations used to calculate fuel matrix degradation.
The Mixed Potential Module (MPM), which provides the rate of fuel matrix degradation
(accounts for both oxidative and chemical dissolution).
The Instant Release Fraction (IRF), which provides the masses of key radionuclides that
will be released from the fuel promptly after the time of exposure (release rate is more
rapid than predicted matrix degradation rate).
The relationship between the FDM and generic performance assessment models is summarized
in Figure 7.1. More details on the information flows involved in the coupling of the process
modules is shown in Figure 4.1.
Used Fuel Degradation: Experimental and Modeling Report October 2013 47
Figure 7.1. Summary information flow diagram showing the relationship of the FDM to the
system-level model and sub-models (modules) comprising the FDM.
Within the context of the higher-level project goal discussed above, the two main objectives of
the work presented in this report are to: (1) develop and implement a new section of code within
the MPM that accounts for the catalyzed oxidation of dissolved hydrogen at the fuel surface, (2)
develop a strategy for coupling the RM and MPM and (3) perform a suit of electrochemical
experiments to inform and test the mixed potential module of the FDM.
7.2 Mixed Potential Module and Surface Catalysis of Redox Reactions
It has been shown experimentally that the noble metal-bearing, fission product alloy phase
(epsilon metal) in used oxide fuel can catalyze redox reactions in aqueous solutions and thus
Used Fuel Degradation: Experimental and Modeling Report 48 October 2013
influence the rate of oxidative dissolution of the fuel matrix (e.g., Broczkowski et al., 2005,
Shoesmith, 2008, Trummer, et al., 2009, Cui et al., 2010). As this process may strongly
influence the degradation rate of used fuel in a geologic repository, it has been incorporated into
the Mixed Potential Module (MPM) of the Fuel Degradation Model. The new module affords
two important capabilities:
Evaluation of the catalytic effects of the noble metal bearing, fission product alloy phase
(Noble Metal Particles - NMP) on reactions affecting fuel matrix degradation.
Evaluation of the long-term importance of H2 oxidation in protecting used fuel from
oxidative dissolution in disposal environments of interest.
The details of the implementation of the MPM are covered in Jerden et al., 2012 and Jerden et
al., 2013, however some background is given here to provide context for the implementation of
the new module.
The MPM is adapted from the Canadian-mixed potential model for UO2 fuel dissolution (King
and Kolar, 1999, King and Kolar, 2003, Shoesmith et.al., 2003) and was implemented using the
numerical computing environment and programming language MATLAB (Jerden et al., 2013).
The MPM is a 1-dimensional reaction-diffusion model that accounts for the following processes:
Rate of oxidative dissolution of the fuel matrix as determined by interfacial redox
reaction kinetics (quantified as a function of the corrosion potential) occurring at the
multiphase fuel surface (phases include UO2 and the noble metal fission product alloy
phase (often called the epsilon phase).
Chemical or solubility-based dissolution of the fuel matrix.
Complexation of dissolved uranium by carbonate near the fuel surface and in the bulk
solution.
Production of hydrogen peroxide (the dominant fuel oxidant in anoxic repository
environments) by alpha-radiolysis.
Diffusion of reactants and products in the groundwater towards and away from the
reacting fuel surface.
Precipitation and dissolution of a U–bearing corrosion product layer on the fuel surface.
Diffusion of reactants and products through the porous and tortuous corrosion product
layer covering the reacting fuel surface.
Arrhenius-type temperature dependence for all interfacial and bulk reactions.
These key processes that are accounted for in the MPM are summarized in Figure 7.2.
Used Fuel Degradation: Experimental and Modeling Report October 2013 49
Figure 7.2. Key processes accounted for in the MPM. The corrosion layer is modeled as a set of
parallel pores with fixed porosity and tortuosity. The noble metal particles (NMP) are modeled
as reactive separate surface domain with its own set of surface reactions.
Calculating the alpha dose rate (and thus H2O2 concentration) for corroding UO2 fuel is
complicated by the effects of U(VI) corrosion products (modeled as schoepite, UO3•2H2O in
MPM). The U(VI) corrosion product layer has three effects on the rate of fuel degradation
predicted by the MPM:
Slows rate of oxidative dissolution by decreasing the reactive surface area of the fuel
(blocking or masking reaction sites).
Slows rate of oxidative dissolution by blocking alpha-particles from interacting with
water and producing radiolytic oxidants (decreases total moles H2O2 produced near fuel
surface). The magnitude of this effect is proportional to surface coverage of corrosion
layer.
Corrosion layer can slow the rate of oxidative dissolution by slowing the rate of diffusion
of oxidants to the fuel surface: U(VI) layer is a tortuous porous mass of crystals
(simulated in MPM by a parallel pores with constant tortuosity).
All three of these effects are modeled in the MPM by a radiolysis "sub-routine" that was recoded
from the original Canadian mixed potential model (for details see Jerden et al., 2013). As in
Canadian model, alpha-particles are currently assumed to have a constant energy of 5.3 MeV and
a solution penetration distance (PEN) of 35 µm in the current MPM. The modeler can set the
penetration distance over the range of PEN = 45 micrometers for ~6.0 MeV alpha-particles down
to PEN = 10 m for ~2.3 MeV particles (King and Kolar, 1999), and the default generation value
Used Fuel Degradation: Experimental and Modeling Report 50 October 2013
for hydrogen peroxide produced by alpha-radiolysis is assumed to be 1.021E-4 mole/Gy/m3
(Christensen and Sunder, 2000). Scoping work to take into account the spatial variation of dose
and radiolysis has been completed and will likely be implemented in a revision of the coupled
RM and MPM.
In the MPM, the fuel degradation rate is calculated using mixed potential theory to account for
all relevant redox reactions at the fuel surface, including those involving oxidants produced by
solution radiolysis; radiolytic processes are quantified in the RM of the FDM. Because the MPM
is based on fundamental chemical and electrochemical principles, it is flexible enough to be
applied to the full range of repository environments as well as shorter-term storage scenarios
being considered as part of the UFD campaign. The current module was developed to model
granitic systems and includes reactions tracking H2, O2, and H2O2, but reactions involving
species important in other disposal systems of interest can be readily incorporated.
The process of interest for this report, and the experimental approach we have used to study it,
are summarized in Figure 7.3. The process involves the catalyzed oxidation of hydrogen on the
NMP surface and the transfer of electrons from NMP sites to the fuel matrix. The electrical
coupling between NMP and fuel grains sets up a galvanic link that effectively protects the fuel
from oxidative dissolution. That is, electrons supplied by hydrogen oxidation effectively
counteract the oxidation of U(IV) to U(VI) by hydrogen peroxide or other oxidants (Figure 7.3).
The new sections of code added to the MPM (Appendix 1) to quantify reactions involving H2
further extend the model’s flexibility and versatility by accounting for the following:
Oxidation of dissolved H2 and H2O2 catalyzed by NMP at the used fuel/solution interface.
The surface area of NMPs, which are treated as a separate electrochemical domain
(phase) at the used fuel/solution interface. The "size" of the NMP domain (relative to the
fuel) is specified by the user in terms of a surface coverage and is electrically linked with
the UO2 matrix by a user adjustable resistance. This will allow the effects of corrosion
and sorption on the catalytic efficiency of the NMPs to be taken into account.
Used Fuel Degradation: Experimental and Modeling Report October 2013 51
Figure 7.3. Schematic diagram showing flow of electrons for surface catalyzed oxidation of
hydrogen. The diagrams on left shows the processes being implemented as part of the MPM.
The diagrams on the right show a simplified conceptual view of the processes and set-up that
was used to perform the electrochemical experiments (experimental results presented below).
7.3 Implementation of Noble Metal Particle Catalyzed Redox Reactions within the Mixed Potential Module
The lines of MATLAB code used to implement the surface catalysis of redox reactions are
shown in Appendix 1. As stated above and shown schematically in Figure 7.3, the catalyzed
reaction occur on separate NMP domains distributed across the fuel surface with the surface
coverage and resistance relative to the fuel matrix set by the modeler. The key reactions
accounted for in the MPM are shown in Table 3.1. This table also identifies the four surface
catalyzed reactions associated with the NMP domain.
Used Fuel Degradation: Experimental and Modeling Report 52 October 2013
To add the reactions catalyzed on the NMP surface (top four reactions in Table 3.1) the
parameter database for the MPM was expanded and updated with appropriate charge transfer
coefficients, rate constants, standard potentials, diffusion coefficients and activation energies for
temperature dependencies for the species/reactions of interest. The parameter values used, which
are shown in Appendix 1, were estimated based on comparisons with similar redox reactions
discussed in King and Kolar, 1999, King and Kolar, 2003, Shoesmith et.al., 2003. A critical
review, based on up-to-date literature, of all parameters and constants used in the MPM is
recommended; however, experiments are also needed to test model results and reduce parameter
uncertainties.
To test the implementation of the NMP domain catalysis process, a number of new MPM runs
were performed. The model inputs for these runs are listed in Table 7.1. Results are shown in
Figures 7.4 – 7.7 and discussed below.
Table 7.1. Parameter and variable inputs used for MPM runs presented below.
Inputs specific to NMP domain
Surface coverage of NMP 1% of fuel surface
Resistance between UO2 and NMP domains 1.0E-3 V/Amp
Concentration of dissolved H2 zero – 1 moles/L
Other user-defined inputs and parameters
Length of model diffusion grid 5 mm
Number of calculation nodes (points) in diffusion grid 200
Duration of simulation 10,000 years
Alpha-particle penetration depth 35 micrometers
Generation value for H2O2 1.021E-4 mole/Gy/m3
Porosity factor for corrosion layer 50%
tortuosity factor for corrosion layer 0.01
Variables
Temperature 25oC (constant)
Dose rate 0.1 Gy unless otherwise noted
Environmental concentration of O2 1.0E-9 moles/L
Environmental concentrations of carbonate and iron Zero
Figure 7.4 shows examples of time-dependent fuel corrosion potentials and corresponding
degradation rates predicted by the MPM for five different dissolved hydrogen concentrations
with 1% NMP at the fuel surface. The model predicts that when hydrogen concentrations greater
than 1.0E-2 moles/L are present at the reacting fuel surface the corrosion potential drops to less
than -0.3 Volts relative to the saturated calomel electrode (VSCE). This corresponds to a fuel
degradation rate of less than 1.0E-5 g/m2/year, which approaches the rate of non-oxidative,
diffusion-driven, chemical dissolution of the fuel. Therefore, according to the MPM,
concentrations around 1.0E-2 molar hydrogen can drive the surface potential of the fuel to below
the threshold for oxidative dissolution. This is consistent with Shoesmith, 2008.
Used Fuel Degradation: Experimental and Modeling Report October 2013 53
The bottom plot in Figure 7.4 highlights the effect that a corrosion layer has on the fuel
degradation rate. For the case with no dissolved hydrogen (yellow), the corrosion layer is
predicted to begin to form around 2 years into the simulation. The layer blocks half of the fuel
surface from emitting alpha radiation into the near-surface solution, thus decreasing (by half) the
amount of hydrogen peroxide (the dominant fuel oxidant) produced within a given time step.
The alpha emission to the solution is decreased by a half because the porosity of the corrosion
layer is assumed to be 50%, that is 50% of the surface is masked by the alpha blocking corrosion
phase. The layer also moderates diffusion due to pore tortuosity. These two effects cause the
transitory decrease in fuel degradation rate seen between 2 – 200 years of the simulation.
Beyond 200 years, the layer thickness exceeds the alpha penetration depth and the generation
and diffusion rates reach steady state.
The bottom plot of Figure 7.4 also shows that even at modest hydrogen concentrations higher
than 1.0E-4 mole/L the corrosion potential and corresponding degradation rates are low enough
to delay the onset of corrosion layer precipitation to beyond 1500 years. At 1.0E-3 moles/L
dissolved hydrogen the fuel degradation rate is too slow to saturate the solution with respect to
the UO3:2H2O corrosion phase (diffusion occurs faster than generation) so no layer forms.
Figure 7.5 shows how the concentration of hydrogen peroxide produced by alpha radiolysis
varies as a function of distance away from the fuel surface. Each point in the plot represents an
individual model calculation in time and space. The competing processes that determine the
shapes and magnitudes of these concentration profiles are:
H2O2 is continuously produced within the first 35 micrometers of the fuel surface (energy
deposition is presently modeled to be uniform within this zone).
H2O2 diffuses towards or away from the fuel surface depending on the concentration
provide, and diffusion rates near the surface will be moderated by the corrosion layer.
H2O2 concentration at environmental boundary (5 mm from fuel) is zero.
H2O2 is consumed (dominantly) at the fuel surface by the following coupled half-
reactions:
o H2O2 + 2e- → 2OH
-
o UO2 → UO22+
+ 2e-
H2O2 consumption rate at the fuel surface increases significantly when the NMP
catalyzed hydrogen oxidation reaction is taken into account and [H2] ≥ 1.0E-4 mole/L
(left side of Figure 7.5):
o H2 + 2OH- → 2H2O + 2e
-
The increase in the rate of hydrogen peroxide consumption at the fuel surface when rapid (NMP-
catalyzed) hydrogen oxidation is occurring is caused by the kinetic balance of the associated
redox reactions (shown in bullets above). Specifically, the large anodic current associated with
the hydrogen oxidation reactions drives up the rate of the dominant cathodic reaction involving
hydrogen peroxide reduction. Therefore, when enough hydrogen is present at a fuel surface
bearing active NMP sites, hydrogen peroxide is rapidly depleted thus decreasing the rate of
oxidative dissolution. That this process of hydrogen oxidation essentially protects the fuel from
degradation is evident in Figure 7.6, which shows the current densities of the key reactions for a
Used Fuel Degradation: Experimental and Modeling Report 54 October 2013
range of hydrogen concentrations. The anodic half-reactions are shown on the top plot of Figure
7.6, while the cathodic half-reactions are shown on the bottom plot.
As the concentration of hydrogen at the fuel surface is increased to ≥ 1.0E-3 mole/L the anodic
current density of the hydrogen oxidation reaction increases from near zero to around 6.6E-5
Amps/m2, while the current density of fuel oxidation reaction decreases from around 4.7E-5
Amps/m2 down to around zero. The corresponding hydrogen peroxide reduction (cathodic)
current density increases from -5.3E-5 Amps/m2 up to -6.3E-5 Amps/m
2 at hydrogen
concentrations ≥ 1.0E-4 mole/L. Also as shown on Figure 7.6, the roles of hydrogen peroxide
oxidation (dark green, top) and oxygen reduction (light blue, bottom plot) are less important to
the overall kinetic balance for the conditions under investigation.
Figure 7.7 shows how increasing the hydrogen concentration at the fuel surface influences the
fuel corrosion potential and degradation rate for two typical dose rates. These plots are
consistent with the observation that once the dissolved hydrogen reaches 0.01 mole/L (with 1%
surface coverage of NMP) the corrosion potential of the fuel drops below the threshold for
oxidative dissolution and the fuel degradation rate is determined by diffusion-driven, chemical
dissolution (~1.0E-7 g/m2/year).
Used Fuel Degradation: Experimental and Modeling Report October 2013 55
Figure 7.4. Examples of time-dependent fuel corrosion potentials and corresponding degradation
rates calculated with the MPM for different dissolved hydrogen concentrations with 1% NMP at
the fuel surface.
Used Fuel Degradation: Experimental and Modeling Report 56 October 2013
Figure 7.5. Concentration profiles of hydrogen peroxide produced by alpha radiolysis as a
function of distance away from the fuel surface. Each point in the plot is an individual model
realization in time and space.
Used Fuel Degradation: Experimental and Modeling Report October 2013 57
Figure 7.6. Current densities for the key reactions over a range of hydrogen concentrations. The
anodic reactions are shown on the top plot, the cathodic reactions are shown on the bottom plot.
Used Fuel Degradation: Experimental and Modeling Report 58 October 2013
Figure 7.7. Fuel corrosion potential and dissolution rate as function of hydrogen concentration
for two typical dose rates. Surface coverage of NMP is set at 1%, for other assumptions see
Table 7.1 above.
Used Fuel Degradation: Experimental and Modeling Report October 2013 59
8. SUMMARY OF ELECTROCHEMICAL EXPERIMENTS
Continuing the suite of tests discussed in Ebert et al., (2012), various electrochemical
experiments were conducted to support the development and extension of the MPM.
Experimental methods are being developed and optimized to:
Verify the conceptual model for fuel matrix degradation that is being used.
Identify important reactants in relevant environments.
Quantify the effects of redox reactions on the corrosion potential at the fuel surface and
the fuel matrix dissolution rate.
Measure values for model parameters.
Measure the effects of corrosion and poisoning on the catalytic efficiency of the NMP
alloys.
An electrochemical system and testing methodology is being developed in which the dissolution
of ceramic UO2 materials representing used fuel are measured in controlled environments under
floating or fixed potentials is measured directly (i.e., based on the dissolved U concentrations)
and related to the measured electrochemical behavior and model parameter values used to
calculate the U(IV) oxidation rate. The experimentally measured rate is based on direct
measurements of the dissolved uranium concentrations and the modeled rate is a convolution of
the rate of the electrochemical (charge-transfer) reaction oxidizing U(IV) to U(VI) and the
dissolution rate of the U(VI)-bearing oxide that is formed.
Parallel experiments are being conducted to study the electrochemical behavior of alloys
representing NMP particles under the same solution conditions that are used to characterize the
UO2 behavior. The experiments are conducted with separate electrodes fabricated from UO2 and
NMP alloy. Experiments are being conducted with the single electrodes to generate a data base
with which the results of future experiments that will be conducted with electrically and
chemically coupled electrodes to measure the dissolution behavior and kinetics of UO2 in the
presence of NMP alloys to quantify the catalytic efficiency of the NMP surfaces. The use of
separate UO2 and NMP electrodes provides flexibility to measure several effects likely to be
important to the long-term corrosion behavior of used fuel: the effects of alloy corrosion and
the presence of poisons on the catalytic efficiency of the NMP can be quantified and taken into
account in the degradation model; the catalytic efficiencies of different NMP compositions (e.g.,
to represent different burn-ups) can be measured; and the corrosion behaviors of UO2 doped with
various lanthanides and actinides can be compared.
Experiments to-date were conducted to develop the methodology, characterize the
electrochemical properties of the isolated UO2 and NMP materials in H2O2-bearing solutions,
and develop techniques for monitoring H2O2 and uranium concentrations during and after
testing. A series of open circuit potential, potentiodynamic, Tafel, linear polarization, and
electrochemical impedance spectroscopy measurements have been made using electrodes
fabricated from pure UO2 and NMP-W alloy materials in solutions with various amounts of H2O2
in air saturated 0.1 mM NaCl solutions and in the same solutions purged with argon or
regeneration gas (regen), which is about 3% H2 in Ar. These measurements provide baseline
values for corrosion potentials and corrosion currents for a wide range of H2O2 concentrations to
which the results of later tests with the combined UO2 and various NMP alloys to quantify the
catalytic effects.
Used Fuel Degradation: Experimental and Modeling Report 60 October 2013
The electrochemical experimental results have been compiled for use as a data base supporting
the MPM as a collection of Microsoft EXCEL files. These have been entered into the document
management system maintained for the DOE FCRD project at the Idaho National Laboratory
under the same document number as this report. An index of the files as organized and the
information contained is presented in Appendix 2. Analyses of several experiments remain in
progress and will be reported in a later report.
9. SUMMARY AND FUTURE WORK ON MPM
A process model for the surface catalysis of key redox reactions on noble metal bearing fission
product alloy particles (NMP) was implemented within the Mixed Potential Module (MPM).
The MPM is part of a larger integrated process level Fuel Degradation Model (FDM) which will
provide information needed for radionuclide source term calculations used in the UFD generic
repository performance assessment model.
The catalytic effects added to the MPM afford two important capabilities:
Evaluation of the catalytic effects of the NMP on reactions affecting fuel matrix
degradation.
Evaluation of the long-term importance of H2 oxidation in protecting used fuel from
oxidative dissolution in disposal environments of interest.
The extension of the MPM to account for NMP catalysis successfully achieves one of the key
goals for this project. However, large uncertainties remain and more experimental and modeling
work is needed to fully quantify the fuel-protecting, hydrogen oxidation effect.
In support of model optimization and extension, electrochemical experiments were performed.
Results from these tests are also presented in this report. The experimental work is focused on
providing key model parameter values needed to improve predictive accuracy and capabilities of
the MPM and thus the FDM.
The scope highlights for FY-2014 (focus of top three bullets) and out-years (all bullets):
Implement integrated FDM consisting of the coupled MPM – Radiolysis Module (RM)
and the Instant Release Fraction (IRF). This integrated model has been developed in
concept (Figures 7.1 and 4.1 and Buck et al., 2013) but not yet implemented.
Link FDM with UFD generic performance assessment models (Figures 7.1 and 4.1
above) to provide a scientific basis for radionuclide source terms.
Tailor MPM – RM parameter database to account for solution chemistry specific to
geologic repositories in argillite and crystalline rocks. This will involve extending the
MPM to lower pH values and may involve adding speciation and redox reactions that
account for components not currently included such as sulfate and dissolved silica.
Develop a predictive understanding of the effects of corrosion and poisoning on the
catalytic activity of the NMP. This work will emphasize the role of halides (F, Cl, Br, I),
the effects of leaching Mo and Tc and the possible formation of Ru, Tc sulfides.
Extend MPM to account for redox chemistry of key dose contributing radionuclides such
as Tc, I, Np, and Pu at the fuel/solution interface.
Used Fuel Degradation: Experimental and Modeling Report October 2013 61
Extend MPM to account for effects of other alteration phases on used fuel degradation
rate. This work will consider the incorporation of alpha emitters into alteration phases
such as U(VI) silicates and U(VI) peroxides.
A crucial part of this work beyond FY-2014 is to continue the matrix of planned electrochemical
and related experiments. Experimental results are needed to reduce uncertainties in the MPM –
RM parameter database and to test model concepts. This work will improve the accuracy of
source term calculations for future repository performance assessments.
Used Fuel Degradation: Experimental and Modeling Report 62 October 2013
10. REFERENCES (Sections 7 through 9)
Broczkowski, M. E., Noël, J. J., Shoesmith, D. W., (2005). The inhibiting effects of hydrogen on
the corrosion of uranium dioxide under nuclear waste disposal conditions, Journal of
Nuclear Materials 346, 16
Buck E., Jerden, J., Ebert, W., Wittman, R, (2013). Coupling the Mixed Potential and Radiolysis
Models for Used Fuel Degradation. FCRD-UFD-2013-000290
Christensen, H., Sunder, S. (1996). An evaluation of water layer thickness effective in oxidation
of UO2 fuel due to radiolysis of water, Journal of Nuclear Materials 238: 70-77.
Ebert, W. L., Cruse, T. A., and Jerden J., (2012). Electrochemical Experiments Supporting Oxide
Fuel Corrosion Model. FCRD-UFD-2012-000201
Jerden, J., Frey, K., Cruse, T., and Ebert, W. (2012). Waste Form Degradation Model Status
Report: Electrochemical Model for Used Fuel Matrix Degradation Rate. FCRD-UFD-
2012-000169.
Jerden, J., Frey, K., Cruse, T., and Ebert, W. (2013). Waste Form Degradation Model Status
Report: ANL Mixed Potential Model, Version 1. Archive. FCRD-UFD-2013-000057.
King, F. and Kolar, M. (1999) “Mathematical Implementation of the Mixed-Potential Model of
Fuel Dissolution Model Version MPM-V1.0”, Ontario Hydro, Nuclear Waste Management
Division Report No. 06819-REP-01200-10005 R00.
King, F. and Kolar, M. (2002) “Validation of the Mixed-Potential Model for Used Fuel
Dissolution Against Experimental Data”, Ontario Hydro, Nuclear Waste Management
Division Report No. 06819-REP-01200-10077-R00.
King, F. and Kolar, M. (2003) “The Mixed-Potential Model for UO2 Dissolution MPM Versions
V1.3 and V1.4”, Ontario Hydro, Nuclear Waste Management Division Report No. 06819-
REP-01200-10104 R00.
Shoesmith, D.W., M. Kolar, and F. King (2003). “A Mixed-Potential Model to Predict Fuel
(Uranium Dioxide) Corrosion Within a Failed Nuclear Waste Container” Corrosion, 59,
802-816.
Shoesmith, D. W. (2008). The Role of Dissolved Hydrogen on the Corrosion/Dissolution of
Spent Nuclear Fuel, NWMO TR-2008-19, November 2008 Nuclear Waste Management
Organization, 22 St. Clair Avenue East, 6th
Floor, Toronto, Ontario M4T 2S3, Canada
Trummer, M., Roth, O., and M. Jonsson, M., (2009), H2 Inhibition of Radiation Induced
Dissolution of Spent Nuclear Fuel, Journal of Nuclear Materials 383, 226-230
Used Fuel Degradation: Experimental and Modeling Report October 2013 63
11. GENERATING STRUCTURAL AND THERMODYNAMIC DATA FOR GEOCHEMICAL AND USED FUEL DEGRADATION MODELS: A FIRST-PRINCIPLES APPROACH
11.1.1 Thermodynamic Properties of Uranyl Peroxide Hydrates Corrosion Phases on Spent Nuclear Fuel: Studtite and Metastudtite
11.1.1.1 Background
Thermodynamic parameters for corrosion phases, as well as engineered barrier systems materials
and natural system minerals, are critical to assess their stability and behavior in geologic disposal
environments for safety assessments. Metal-oxides constituting most of the spent nuclear fuel
(SNF) are particularly prone to redox corrosion and dissolution, which is pervasive and of
critical significance for environmental systems (Stumm, Sigg, and Sulzberger, 1992).
Oxidative dissolution of SNF leads to the formation of uranyl-based phases. The uranyl phases
likely to form are primarily oxide hydrates, as well as a rich variety of other silicates, phosphates
and carbonates, depending on the local natural system environment. Over fifty uranyl
minerals/phases occur in nature and as corrosion products of SNF.
Among the corrosion phases that may form on SNF exposed to water, studtite and metastudtite,
with formulas (UO2)O2(H2O)4 and (UO2)O2(H2O)2, respectively, are considered to be of
particular importance (McNamara, Buck, and Hanson, 2003; Hanson, et al.,2005; McNamara,
Hanson, Buck, & Soderquist, 2005). These hydrates of uranyl peroxide, which incorporate (O2)
2-
generated by α-radiolysis of water (Draganic and Draganic, 1971; Sattonnay, et al., 2001;
Amme, 2002), may play a crucial role in the degradation of nuclear fuel in the context of
geological repositories – or nuclear reactor accidents (Hughes-Kubatko, Helean, Navrotsky, and
Burns, 2003; Armstrong, Nyman, Shvareva, Sigmon, Burns, and Navrotsky, 2012; Burns,
Ewing, and Navrotsky, 2012). Studtite and metastudtite are also the only two known minerals
containing peroxide. In addition to playing a role for corrosion of SNF, studtite may retain
released radionuclides through incorporation into its structure (Buck, Hanson, Friese, Douglas,
and McNamara, 2004; Shuller, Ewing, and Becker, 2010).
Due in part to the unique nature of these compounds, the characterization of studtite and
metastudtite evolved rather slowly. The structures of studtite and metastudtite were fully
elucidated only recently (Burns and Hugues, 2003; Ostanin and Zeller, 2007; Weck, Kim, Jové-
Colón, and Sassani, 2012). However, very limited information on the stability and
thermodynamic properties of these compounds is currently available, due to the difficulty of the
calorimetric experiments involving uranyl minerals and compounds (Shvareva, Fein, and
Navrotsky, 2012).
The main objectives of this study, using first-principles methods (without the need for any
experimental input), are to:
Calculate missing thermodynamic data needed for SNF degradation models, as a fast,
systematic, and early way to avoid using expensive and time-consuming real materials
and to complement experiments.
Provide an independent assessment of existing experimental thermodynamic data and
resolve contradictions in existing calorimetric data.
Used Fuel Degradation: Experimental and Modeling Report 64 October 2013
Validate our computational approach using high-quality calorimetric data.
Details of our computational approach are given in the next section, followed by a complete
analysis and discussion of our results.
11.1.1.2 Computational Methods
A schematic representation of the three-step computational approach used in this report is
displayed in Figure 11.1. The first step consists of a crystal structure optimization using density
functional theory (DFT), followed by a calculation of phonon frequencies using density
functional perturbation theory (DFPT), and, finally, a phonon analysis is carried out to derive the
thermodynamics properties of the crystalline system investigated.
Figure 11.1. Schematic representation of the three-step computational approach used to calculate
the thermal properties of crystalline systems using first-principles methods.
The equilibrium structures of studtite and metastudtite, previously optimized (cf. Figure 11.2)
using the standard density functional theory (DFT) implemented in the Vienna Ab initio
Simulation Package (VASP) (Kresse & Furthmüller, 1996), were used to build a set of
supercells; details of the geometry optimization calculations are given in Weck, Kim, Jové-
Colón, and Sassani, 2012. The forces exerted on atoms of the set of supercells were calculated
using density functional perturbation theory (DFPT) with VASP at the GGA/PW91 level of
theory (Perdew & Wang, 1992) and phonon frequencies were computed. Phonon analysis was
performed at constant equilibrium volume in order to derive isochoric thermal properties (e.g.,
the phonon (Helmholtz) free energy, the entropy and the isochoric heat capacity).
Used Fuel Degradation: Experimental and Modeling Report October 2013 65
Figure 11.2. Crystal unit cells of (a) studtite, (UO2)O2(H2O)4 (space group C2/c, Z = 4), and (b)
metastudtite, (UO2)O2(H2O)2 (space group Pnma, Z = 4), relaxed with DFT at the GGA/PW91
level of theory. Color legend: U, blue; O, red; H, white.
The Helmholtz free energy was calculated using the following formula:
∑ ∑ [ ]
The entropy was computed using the expression:
∑ [ ]
∑
The heat capacity at constant volume was calculated using the formula:
∑ [
]
[ ]
Further analysis from a set of phonon calculations in the vicinity of each computed equilibrium
crystal structure was carried out to obtain thermal properties at constant pressure (e.g., the Gibbs
free energy and the isobaric heat capacity) within a quasi-harmonic approximation (QHA). The
QHA mentioned here introduces volume dependence of phonon frequencies as a part of
anharmonic effect. A part of temperature effect can be included into the total energy of electronic
structure through the phonon (Helmholtz) free energy at constant volume, but thermal properties
at constant pressure are what we want to know. Therefore, some transformation from a function
of volume V to a function of pressure p is needed. The Gibbs free energy is defined at a constant
pressure by the transformation:
( )
[ ( ) ( ) ]
where [ ] means to find unique minimum value in the brackets by changing
volume. Since volume dependencies of energies in electronic and phonon structures are different,
volume giving the minimum value of the energy function in the square brackets shifts from the
value calculated only from electronic structure even at T = 0 K. By increasing temperature, the
volume dependence of phonon free energy changes, then the equilibrium volume at temperatures
changes.
The heat capacity at constant pressure versus temperature was also derived as the second
derivative of the Gibbs free energy with respect to T, i.e.:
Used Fuel Degradation: Experimental and Modeling Report 66 October 2013
In order to derive the enthalpy function, ( ) , and the Gibbs energy function,
( ) , the thermal evolutions of the isobaric heat capacity calculated from first-
principles were first fitted using a nonlinear least-squares regression to a Haas-Fisher-type
polynomial, i.e,
( )
The enthalpy function was then computed by analytical integration of the fit to the isobaric heat
capacity using the formula:
( ) ∫ ( )
The Gibbs energy function was then computed using the following expression:
( ) ( )
where ST is the entropy calculated from first-principles.
11.1.1.3 Results and Discussion
The thermal properties (Helmoltz free energy, entropy, isochoric molar heat capacity and total
internal energy) of bulk studtite and metastudtite calculated from phonon frequencies at constant
equilibrium volume at the DFT/DFPT/PW91 level of theory are shown in Figures 11.3 and 11.4,
respectively. To the best of our knowledge, no experimental data are available for the sake of
comparison. The results for the thermal properties of studtite and metastudtite at standard
pressure (1 bar) calculated within the quasi-harmonic approximation, i.e. the Gibbs free energy
and isobaric heat capacity, are displayed in Figures 11.5 to 11.8.
As shown in Figures 11.3 and 11.4, the entropy increases steadily with temperature and with the
unit-cell volume expansion occurring for studtite and metastudtite. This is consistent with the
fact that a temperature or unit-cell volume increase results in a larger number of microstates in
the system, W, which in turn increases logarithmically the entropy according to Boltzmann’s
entropy formula, S = kB .log W, where kB is the Boltzmann constant.
The monotonically decreasing Gibbs free energy curves and their derived isobaric heat capacities
Cp as a function of the temperature are show in Figures 11.5 to 11.8. The predicted Dulong-Petit
asymptotic values of studtite and metastudtite, i.e. Cp = n3R, where n is the number of atoms per
f.u. and R is the universal gas constant, are 424.0 J.K-1
.mol-1
and 274.3 J.K-1
.mol-1
, respectively.
At T = 800 K, the highest boundary of the thermal range investigated here, the computed Cp
values for studtite and metastudtite are still well below their Dulong-Petit asymptotes, i.e. by ca.
25% and 21%, respectively. As expected, Cp[(UO2)O2(H2O)4] > Cp[(UO2)O2(H2O)2] over the
complete temperature range investigated, which is in line with the calculated entropy for both
compounds, since the variation of entropy with T corresponds to the integral of (Cp/T) over a
given temperature range. This stems from the loss of H2O molecules from studite to metastudtite.
Used Fuel Degradation: Experimental and Modeling Report October 2013 67
Figure 11.3. Thermal properties of studtite, (UO2)O2(H2O)4, calculated at constant equilibrium
volume at the DFT/PW91 level of theory. Potential thermal conditions of interest for nuclear
waste disposal in geological repositories are indicated as a shaded area.
Figure 11.4. Thermal properties of metastudtite, (UO2)O2(H2O)2, calculated at constant
equilibrium volume at the DFT/PW91 level of theory. Potential thermal conditions of interest for
nuclear waste disposal in geological repositories are indicated as a shaded area.
Used Fuel Degradation: Experimental and Modeling Report 68 October 2013
Figure 11.5. Gibbs free energy of studtite calculated at constant atmospheric pressure at the
DFT/PW91 level of theory. Potential thermal conditions of interest for nuclear waste disposal in
geological repositories are indicated as a shaded area.
Figure 11.6. Gibbs free energy of metastudtite calculated at constant atmospheric pressure at the
DFT/PW91 level of theory. Potential thermal conditions of interest for nuclear waste disposal in
geological repositories are indicated as a shaded area.
Used Fuel Degradation: Experimental and Modeling Report October 2013 69
Figure 11.7. Heat capacity of studtite calculated at constant atmospheric pressure at the
DFT/PW91 level of theory. Potential thermal conditions of interest for nuclear waste disposal in
geological repositories are indicated as a shaded area.
Figure 11.8. Heat capacity of metastudtite calculated at constant atmospheric pressure at the
DFT/PW91 level of theory. Potential thermal conditions of interest for nuclear waste disposal in
geological repositories are indicated as a shaded area.
Used Fuel Degradation: Experimental and Modeling Report 70 October 2013
The thermal evolutions of the isobaric heat capacity (P = 1 bar) calculated from first-principles
for studtite and metastudtite (see Figures 11.7 and 11.8) were fitted over the temperature range
290–800 K using a nonlinear least-squares regression to a Haas-Fisher-type polynomial, i.e,
( )
with the resulting optimized coefficients given in Table 11.1. The sums of the squared
differences are small, 0.21 for studtite and 0.16 for metastudtite, suggesting a good correlation
between the predicted data and the resulting fits.
Table 11.1. Coefficients of the Haas-Fisher heat capacity polynomial Cp(T) for the studtite and
metastudite compounds. The range of validity of the fit is 290–800 K.
Compound a×102
(T0)
b×10-2
(T)
c×106
(T-2
)
d×103
(T-0.5
)
e×10-5
(T2)
SSDa
Studtite
Metastudtite
5.7999
3.1599
-6.498
-0.405
2.2373512
-0.2250414
-6.51293
-2.70420
2.892
0.187
0.21
0.16
a Sum of squared differences (SSD) between calculated and fitted data.
Figure 11.9. Enthalpy functions and Gibbs energy functions of studtite [(a) and (c)] and
metastudtite [(b) and (d)] calculated at the DFT/PW91 level of theory. Potential thermal
conditions of interest for nuclear waste disposal in geological repositories are indicated as a
shaded area.
Used Fuel Degradation: Experimental and Modeling Report October 2013 71
The enthalpy functions and Gibbs energy functions of studtite and metastudtite were also
calculated by analytical integration of the fit to the isobaric heat capacity and using the entropy
calculated from first-principles as described above; results are displayed in Figure 11.9.
However, to the best of our knowledge, no experimental data are available for the sake of
comparison, and these results are the first theoretical predictions of the thermal properties for
these compounds using a rigorous first-principles methodology.
11.1.2 Structures and Properties of Layered Uranium(VI) Oxide Hydrates: Study of Polymorphism in Dehydrated Schoepite
11.1.2.1 Background
Deciphering the complex interplay between the crystal structures and properties of inorganic
uranyl compounds and uranyl minerals is crucial to gain understanding of the transport and
fixation of uranium in the environment, the paragenesis of uranyl minerals, and the performance
of geological repositories for used nuclear fuel.
Among the known minerals containing hexavalent uranium, the uranyl oxide hydrates, represent
an important subgroup. The crystal structures of most uranyl oxide hydrates are based on sheets
of polyhedra of the form [(UO2)x Oy(OH)z] (2x-2y-z)
. This includes four closely related uranyl oxide
hydrates/hydroxides without interlayer cations that form the schoepite subgroup and the
fourmarierite group: schoepite, metaschoeptite, "paraschoepite" and dehydrated schoepite.
Among these uranyl oxide hydrates/hydroxides without interlayer cations, dehydrated schoepite
was found to have a composition ranging from UO3(H2O)0.75 to UO3(H2O) (Finch, Hawthrone,
and Ewing, 1998) and lead to the formation of studtite in the presence of moisture and hydrogen
peroxide. Assuming an ideal stoichiometry of UO2(OH)2 (or UO3(H2O)) for simplicity, the
experiments conducted so far have shown that dehydrated schoepite is rapidly converted to
studtite upon contact with hydrogen peroxide and moisture according to the reaction:
UO2(OH)2 + H2O2 + 2 H2O [(UO2)(O2)(H2O)2](H2O)2.
Recent experiments have shown that at low concentration of H2O2 (i.e. 0.001 M), a few percents
of the crystalline higher hydrate metaschoepite, UO3(H2O)2, also formed, while higher
concentrations of H2O2 in the range 0.01–0.05 M resulted in a mixture of dehydrated schoepite
and studtite or even complete conversion to studtite for concentrations in excess of 0.1 M H2O2
(Forbes, Horan, Devine, McInnis, and Burns, 2011). Details of such interconversions between
dehydrated schoepite, metaschoepite, and schoepite have been discussed elsewhere (Finch,
Hawthrone, and Ewing, 1998).
Dehydrated schoepite exists in three crystal forms, α, β and γ, which can be prepared
hydrothermally from UO3 and H2O (Dawson, Wait, Alcock, and Chilton, 1956). Using first-
principles methods, polymorphism is investigated in this layered uranium(VI) oxide hydrate. In
particular, computational approaches going beyond the standard DFT framework are utilized
here and include corrections for possible strong on-site Coulomb repulsion between uranium 5f
electrons or for van der Waals dispersion interactions. Details of our computational approach are
provided in the next section, followed by a discussion of our results and conclusions.
11.1.2.2 Computational Methods
First-principles total energy calculations were performed using spin-polarized density functional
theory, as implemented in the Vienna Ab initio Simulation Package (VASP) (Kresse and
Used Fuel Degradation: Experimental and Modeling Report 72 October 2013
Furthmüller, 1996). The exchange-correlation energy was calculated within the generalized
gradient approximation (GGA+U) (Perdew, et al., 1992), with the parameterization of Perdew,
Burke, and Ernzerhof (PBE) (Perdew, Burke, and Ernzerhof, 1996), corrected with an effective
Hubbard parameter to account for the strong on-site Coloumb repulsion between localized
uranium 5f electrons. Standard functionals such as the PBE or PW91 functionals were found in
previous studies to correctly describe the geometric parameters and properties of various
uranium oxides and uranium containing structures observed experimentally (Weck, Kim,
Balakrishnan, Poineau, Yeamans, and Czerwinski, 2007; Weck, Kim, Masci, Thuery, and
Czerwinski, 2010; Weck, Gong, Kim, Thuery, and Czerwinski, 2011; Thompson and Wolverton,
2011; Weck, Kim, Jové-Colón, and Sassani, 2012).
The rotationally-invariant formalism developed by Dudarev and co-workers (Dudarev, Botton,
Savrasov, Humphreys, & Sutton, 1998) was used, which consists in adding a penalty functional
to the standard GGA total-energy functional, , that forces the on-site occupancy matrix in
the direction of idempotency, i.e.
( ̅ )̅
∑ [ ( ) ( )] ,
where ̅ and ̅ are the spherically-averaged matrix elements of the screened electron-electron
Coloumb and exchange interactions, respectively, and is the density matrix of 5f electrons
with a given projection of spin . In Dudarev’s approach only ̅ ̅ is meaningfull.
Therefore, only ̅ was allowed to vary in the calculations.
The interaction between valence electrons and ionic cores was described by the projector
augmented wave (PAW) method (Blöchl, 1994; Kresse and Joubert, 1999). The
U(6s,6p,6d,5f,7s) and O(2s,2p) electrons were treated explicitly as valence electrons in the
Kohn-Sham (KS) equations and the remaining core electrons together with the nuclei were
represented by PAW pseudopotentials. The KS equation was solved using the blocked Davidson
(Davidson, 1983) iterative matrix diagonalization scheme. The plane-wave cutoff energy for the
electronic wavefunctions was set to 500 eV, ensuring the total energy of the system to be
converged to within 1 meV/atom.
Since the structure of dehydrated schoepite consists of stacked UO2(OH)2 layers linked by O–
H…
O(uranyl) hydrogen bonds, it can be inferred that van der Waals dispersion interactions may
play a role in the possible structures and properties of the various polymorphs of this compound.
However, popular density functionals are unable to describe correctly van der Waals interactions
resulting from dynamical correlations between fluctuating charge distributions. A pragmatic
method to work around this problem has been given by density functional theory corrected for
dispersion (DFT-D) (Wu, Vargas, Nayak, Lotrich and Scoles, 2001), which consists in adding a
semi-empirical dispersion potential to the conventional Kohn-Sham GGA total-energy
functional, , i.e.,
.
In the DFT-D2 method of Grimme (Grimme, 2006) utilized in this study, the van der Waals
interactions are described via a simple pair-wise force field, which is optimized for DFT
functionals. The dispersion energy for periodic systems is defined as:
∑ ∑ ∑
| ⃗ ⃗ | (| ⃗ ⃗ |)
,
Used Fuel Degradation: Experimental and Modeling Report October 2013 73
where the summation are over all atoms and all translations of the unit cell ( ),
with the prime sign indicating that cell for , is a global scaling factor,
is the
dispersion coefficient for the atom pair , ⃗ is a position vector of atom after performing
translations of the unit cell along lattice vectors. In practice, terms corresponding to interactions
over distances longer than a certain suitably chosen cutoff radius contribute only negligibly to
the dispersion energy and can be ignored. The term ( ) is a damping function:
( )
(
⁄ )
,
whose role is to scale the force field such as to minimize contributions from interactions within
typical bonding distances. Combination rules for dispersion coefficients
and van der Waals
radii
are:
√
,
and
.
The global scaling parameter has been optimized for several different DFT functionals and
corresponds to a value of for the PBE functional used in this study. The parameters
used in the empirical force-field of Grimme (Grimme, 2006) are Å and
Jnm6.mol
-1 for hydrogen and Å and Jnm
6.mol
-1 for oxygen.
In this work, both the GGA+U and GGA-DFT-D methods are also used concurrently, therefore,
the resulting total-energy functional can be expressed as:
( ̅ )̅
∑ [ ( ) ( )] ,
where all the notations used keep the same meaning as defined previously.
All structures were optimized with periodic boundary conditions applied. Ionic relaxation was
carried out using the quasi-Newton method and the Hellmann-Feynman forces acting on atoms
were calculated with a convergence tolerance set to 0.01 eV/Å. Structural optimizations and
properties calculations were carried out using the Monkhorst-Pack special k-point scheme
(Monkhorst & Pack, 1976) with 5×3×5, 5×5×3 and 5×5×5 meshes for integrations in the
Brillouin zone (BZ) of the bulk α–, β–, and γ–UO2(OH)2 phases, respectively. The tetrahedron
method with Blöchl corrections (Blöchl, Jepsen, and Andersen, 1994) was used for BZ
integrations. Periodic unit cells containing 28 atoms (Z = 4) for the α and β phases and 14 atoms
(Z = 2) for the γ phase were used in the calculations. Ionic and cell relaxations of the
experimental bulk structures (Bannister and Taylor, 1970; Taylor and Hurst, 1971; Taylor, Kelly
and Downer, 1972; Siegel, Hoekstra, and Gebert, 1972) were performed simultaneously, without
symmetry constraints.
11.1.2.3 Results and Discussion
The crystal parameters for UO2(OH)2 were determined originally from XRD by Taylor and co-
workers (Bannister and Taylor, 1970; Taylor and Hurst, 1971; Taylor, 1971; Taylor, Kelly and
Downer, 1972) and others (Roof, Cromer and Larson, 1964; Siegel, Hoekstra, and Gebert, 1972).
Used Fuel Degradation: Experimental and Modeling Report 74 October 2013
For α-UO2(OH)2: a = 4.2455(6), b = 10.3183(16), c = 6.8648(10) Å, α = β= γ =90°, V = 300.7(l)
Å3, Z = 4, and space group Cmca (IT No. 64) or C2cb (IT No. 41); for β-UO2(OH)2: a =
5.6438(l), b = 6.2867(l), c = 9.9372(2) Å, α = β= γ =90°, V = 352.58(2) Å3, Z = 4, and space
group Pbca (IT No. 61); for γ-UO2(OH)2: a = 5.560(3), b = 5.522(3), c = 6.416(3) Å, α = γ =90°,
β=112.71(9)°, V = 181.71 Å3, Z = 2, and space group P21/c (IT No. 14).
In the α phase, the UO2(OH)2 layers are linked by O-H…
O (uranyl) hydrogen bonds and the
uranium coordination number is eight, with a puckered hexagonal arrangement (Taylor, 1971).
In the β phase, the uranium centers possess a coordination of six in with octahedral arrangement
and the the stacked UO2(OH)2 layers are also linked by O-H…
O (uranyl) hydrogen bonds
(Bannister and Taylor, 1970). The location of hydrogen atoms in the α and β phases were
confirmed by the neutron powder diffraction studies of Taylor and Hurst (Taylor and Hurst,
1971). In the γ phase, the configuration about uranium atoms is a distorted octahedron with
variable U-O distances and the overall structure show strong similarity to β-UO2(OH)2.
Figure 11.10. Crystal unit cells of the (a) alpha-, (b) beta- and (c) gamma phases of dehydrated
schoepite, UO2(OH)2, relaxed with DFT at the GGA/PBE level of theory. Color legend: U, blue;
O, red; H, white.
Crystal unit cells of the α, β, and γ phases of dehydrated schoepite relaxed with DFT at the
GGA/PBE level of theory are depicted in Figure 11.10. The optimized structures are in overall
good agreement with the three structures characterized experimentally. Using standard DFT, the
following lattice parameters were obtained: 1) α-UO2(OH)2: a = 4.233, b = 10.344, c = 6.970 Å,
α = β= γ =90°, V = 305.2 Å3; 2) β-UO2(OH)2: a = 5.848, b = 6.204, c = 9.867 Å, α = β= γ =90°,
V = 358.0 Å3; 3) γ-UO2(OH)2: a = 5.891, b = 5.322, c = 6.369 Å, α = γ =90°, β=113.8°, V =
182.73 Å3. Since some small discrepancies subsist between parameters computed with standard
DFT and values determined with XRD the influence of possible van der Waals interactions and
strong electron correlation was investigated for α-UO2(OH)2 using DFT-D2 and DFT+U
simultaneously. The evolution of the computed volume and lattice parameters of α-UO2(OH)2 as
functions of the effective Hubbard parameter is shown in Figure 11.11, and the corresponding
evolution of the computed U-O, O-H and O…
H bond distances is displayed in Figure 11.12.
Used Fuel Degradation: Experimental and Modeling Report October 2013 75
Figure 11.11. Evolution of the computed volume and lattice parameters of α-UO2(OH)2, as
functions of the effective Hubbard parameter, Ueff. Calculations were carried out at the
GGA+U/PBE level of theory, with (DFT-D) and without inclusion of dispersion corrections
(DFT). Experimental values (Taylor and Hurst, 1971) are also reported for the sake of
comparison.
Used Fuel Degradation: Experimental and Modeling Report 76 October 2013
Figure 11.12. Evolution of the computed U–O, O–H and O…
H bond distances in α-UO2(OH)2,
as functions of the effective Hubbard parameter, Ueff. Calculations were carried out at the
GGA+U/PBE level of theory, with (DFT-D) and without inclusion of dispersion corrections
(DFT).
As shown in Figure 11.11, ramping up the +U parameter as for effect to systematically increase
the in-plane lattice parameters a and b of the UO2(OH)2 sheets and therefore also increase the
volume of the unit cell. On the other hand, including a dispersion correction term through the use
of DFT-D2 slightly reduces the volume and lattice parameters relative to standard DFT results.
Used Fuel Degradation: Experimental and Modeling Report October 2013 77
However, DFT-D2 calculations still overestimate the interlayer spacing along the c axis by about
1%, although they tend slightly improve the agreement between the computed and measured unit
cell volume for U = 0 eV. The present DFT+U results, with or without inclusion of a dispersion
correction, also suggest that no strong electron correlation term is needed and the phases of
UO2(OH)2 can be investigated using standard DFT. A similar assumption was previously utilized
successfully in the study of studtite and metastudtite with U(VI) metals centers (Weck, Kim,
Jové-Colón, and Sassani, 2012); however, such approximation is found to be invalid for bulk
UO2 with U(IV) metal centers. As depicted in Figure 11.12, the DFT+U and DFT-D methods
also have limited effect on the computed bond distances.
Figure 11.13. X-ray diffraction pattern of α-UO2(OH)2. The experimental powder diffraction
pattern for Cu Kα1 radiation (Taylor and Hurst, 1971) is represented by a black line. The
diffraction pattern simulated from the structure relaxed with DFT/PBE reported in the present
study is shown in red. A full-width at half-maximum (FWHM) parameter of 0.2 2θ was used in
the simulation. The XRD pattern recorded for paulscherretite, the mineral form of dehydrated
schoepite (Brugger et al., 2011), is also reported for the sake of comparison.
Since the DFT-D approach only slightly improves the agreement between calculated and
experimental lattice parameters, without matching the interlayer spacing between α-UO2(OH)2
sheets, it was decided alternatively to use the lattice parameters determined with XRD and relax
ionic positions without symmetry constraints applied. The diffraction pattern simulated from the
α-UO2(OH)2 structure relaxed with DFT/PBE is shown in Figure 11.13 along with the XRD
Used Fuel Degradation: Experimental and Modeling Report 78 October 2013
pattern collected for Cu Kα1 radiation (Taylor and Hurst, 1971). Excellent agreement is obtained
between experiment and theory. For the sake of comparison, the XRD pattern recorded for
paulscherretite, the mineral form of dehydrated schoepite (Brugger et al., 2011), has also been
reported. Some small peak mismatch with the results of Taylor and Hurst and our results for pure
dehydrated schoepite can be seen for large 2θ angles owing to the presence of metaschoepite in
the paulscherretite mineral (Brugger et al., 2011). The structures of the β, and γ phases of
dehydrated schoepite have also been reoptimized using the fixed lattice parameters determined
with XRD. The three resulting UO2(OH)2 phases will be used in future calculations of the
thermodynamic stability and phase transitions in this compound.
12. CONCLUSIONS
Density functional theory (DFT) calculations of the thermodynamic properties of crystalline
studtite, (UO2)O2(H2O)4, and metastudtite, (UO2)O2(H2O)2, were carried out within the generalized
gradient approximation. Specifically, phonon analysis using density functional perturbation
theory was carried out in order to derive both their isochoric and isobaric thermal properties.
Further experimental work is needed to assess our theoretical predictions for these SNF
corrosion phases. This methodology will be applied in a systematic way to other possible
metastable corrosion phases and other NS and EBS models to expand the applicability of this
data set to more realistic systems. Such an expanded data set will facilitate investigation of
nuclear waste disposal in geological repositories.
In addition, polymorphism in stoichiometric dehydrated schoepite, UO2(OH)2, was investigated
using computational approaches that go beyond standard DFT and include van der Waals
dispersion corrections (DFT-D) and strong-electron correlation (DFT+U). As experiments
conducted so far have shown, dehydrated schoepite can rapidly converted to studtite upon
contact with hydrogen peroxide and moisture and might therefore play a role as a precursor to
the formation of studtite on the surface of SNF. The present study shows that standard DFT is
sufficient to investigate, since DFT+U and DFT-D methods have limited effect on the computed
bond distances and only the DFT-D approach slightly improves the agreement between
calculated and experimental lattice parameters. The three UO2(OH)2 phases optimized with
standard DFT will be used in future calculations of the thermodynamic stability and phase
transitions in this compound.
13. REFERENCES (Sections 11 through 12)
Amme, M. (2002). “Contrary effects of the water radiolysis product H2O2 upon the dissolution of
nuclear fuel in natural ground water and deionized water”. Radiochimica Acta, 90(7), 399–406.
Armstrong, C., M. Nyman, T. Shvareva, G. Sigmon, P. Burns, and A. Navrotsky (2012). “Uranyl
peroxide enhanced nuclear fuel corrosion in seawater”. Proceedings of the National Academy of
Sciences of the USA, 109(6), 1874–1877.
Bannister, M. J., and J. C. Taylor (1970). “The crystal structure and anisotropic thermal
expansion of β-uranyl dihydroxide, UO2(OH)2”. Acta Crystallogr., B26, 1775–1781.
Blöchl, P. (1994). “Projector Augmented-Wave Method”. Physical Review B, 50(24), 17953–
17979.
Blöchl, P., O. Jepsen, and O. Andersen (1994). “Improved Tetrahedron Method for Brillouin-
Zone Integrations”. Physical Review B, 49(23), 16223–16233.
Used Fuel Degradation: Experimental and Modeling Report October 2013 79
Brugger, J., N. Meisser, B. Etschmann, S. Ansermet, and A. Pring (2011). “Paulscherrerite from
the Number 2 Workings, Mount Painter Inlier, Northern Flinders Ranges, South Australia:
“Dehydrated schoepite” is a mineral after all”. American Mineralogist, 96, 229–240.
Buck, E., B. Hanson, J. Friese, M. Douglas, and B. McNamara (2004). “Evidence for neptunium
incorporation into uranium (VI) phases”. In J. Hanchar, S. Stroes Gascoyne, & L. Browning
(Ed.), 28th Symposium on the Scientific Basis for Nuclear Waste Management held at the 2004
MRS Spring Meeting. 824, pp. 133-138. San Francisco, CA: Materials Resarch Society
Symposium Proceedings.
Burns, P., and K.-A. Hugues (2003). “Studtite, [(UO2)(O2)(H2O)2](H2O)2: The first structure of a
peroxide mineral”. American Mineralogist, 88(7), 1165–1168.
Burns, P., R. Ewing, and A. Navrotsky (2012). “Nuclear Fuel in a Reactor Accident”. Science,
335(6073), 1184–1188.
Davidson, E. R. (1983). In G. Diercksen, & S. Wilson (Eds.), Methods in Computational
Molecular Physics (Vol. 113, p. 95). New York, NY: NATO Advanced Study Institute, Series C,
Plenum.
Dawson, J. K, E. Wait, K. Alcock, and D. R. Chilton (1956). “Some aspects of the system
uranium trioxide-water”. Journal of the Chemical Society, Sept., 3531–3540.
Draganic, I., and Z. Draganic (1971). The Radiation Chemistry of Water. New York, NY:
Academic Press.
Dudarev, S., G. Botton, S. Savrasov, C. Humphreys, and A. Sutton (1998). “Electron-energy-loss
spectra and the structural stability of nickel oxide: An LSDA+U study”. Physical Review B,
57(3), 1505–1509.
Finch, R.J., F. C. Hawthorne, and R. C. Ewing (1998). “Structural relations among schoepite,
metaschoepite, and “dehydrated schoepite”. Canadian Mineralogist, 36, 831–845.
Forbes, T. Z., P. Horan, T. Devine, D. McInnis, and P. C. Burns (2011). “Alteration of
dehydrated schoepite and soddyite to studtite, [(UO2)(O2)(H2O)2](H2O)2”. American
Mineralogist, 96, 202–206.
Grimme, S. (2006). “Semiempirical GGA-type density functional constructed with a long-range
dispersion correction”, J. Comp. Chem., 27, 1787.
Hanson, B., B. McNamara, E. Buck, J. Friese, E. Jenson, K. Krupka, et al. (2005). Corrosion of
commercial spent nuclear fuel. 1. Formation of studtite and metastudtite. Radiochim. Acta, 93(3),
159–168.
Hughes-Kubatko, K.-A., K. Helean, A. Navrotsky, and P. Burns (2003). “Stability of peroxide-
containing uranyl minerals”. Science, 302, 1191–1193.
Kresse, G., and J. Furthmüller (1996). “Efficient iterative schemes for ab initio total-energy
calculations using a plane-wave basis set”. Physical Review B, 54(16), 11169–11186.
Kresse, G., and D. Joubert (1999). “From ultrasoft pseudopotentials to the projector augmented-
wave method”. Physical Review B, 59(3), 1758–1775
McNamara, B., E. Buck, and B. Hanson (2003). Observation of studtite and metastudtite on
spent fuel. In R. Finch, & D. Bullen (Ed.), 26th Symposium on the Scientific Basis for Nuclear
Used Fuel Degradation: Experimental and Modeling Report 80 October 2013
Waste Management held at the 2002 MRS Fall Meeting . 757, pp. 401–406. Boston, MA : Mater.
Res. Soc. Symp. Proc.
McNamara, B., B. Hanson, E. Buck, C. Soderquist (2005). Corrosion of commercial spent
nuclear fuel. 2. Radiochemical analyses of metastudtite and leachates. Radiochimica Acta, 93(3),
169–175.
Monkhorst, H., and J. Pack (1976). “Special Points for Brillouin-Zone Integrations”. Physical
Review B, 13(12), 5188–5192
Ostanin, S., and P. Zeller, P. (2007). “Ab initio study of uranyl peroxides: Electronic factors
behind the phase stability”. Physical Review B, 75(7), 073101.
Perdew, J., and Y. Wang (1992). “Accurate and Simple Analytic Representation of the Electron-
Gas Correlation-Energy”. Physical Review B, 45(23), 13244–13249.
Perdew, J., J. Chevary, S. Vosko, K. Jackson, M. Pederson, D. Singh, et al. (1992). “Atoms,
Molecules, Solids, and Surfaces - Applications of the Generalized Gradient Approximation for
Exchange and Correlation”. Physical Review B, 46(11), 6671–6687.
Perdew, J. P., K. Burke, and M. Ernzerhof (1996). “Generalized gradient approximation made
simple”. Physical Review Letters, 77, 3865.
Roof, R. B., D. T. Cromer, and A. C. Larson (1964). “Crystal structure of uranyl dihydroxide
UO2(OH)2”. Acta Crystallographica, 17, 710.
Sattonnay, G., C. Ardois, C. Corbel, J.-F. Lucchini, M.-F. Barthe, F. Garrido, et al. (2001).
Alpha-radiolysis effects on UO2 alteration in water. Journal of Nuclear Materials, 288(1), 11–
19.
Shuller, L., R. Ewing and U. Becker (2010). “Quantum-mechanical evaluation of Np-
incorporation into studtite”. American Mineralogist, 95(8-9), 1151–1160.
Shvareva, T. Y., J. B. Fein, and A. Navrotsky (2012). “Thermodynamic properties of uranyl
minerals: constraints from calorimetry and solubility measurements”. Industrial & Engineering
Chemistry Research, 51, 607–613
Siegel, S., H. R. Hoekstra, and E. Gebert (1972). “Structure of gamma-uranyl dihydroxide,
UO2(OH)2”. Acta Crystallographica B, 28, 3469–3473.
Stumm, W., L. Sigg, and B. Sulzberger (1992). Chemistry of the Solid-Water Interface:
Processes at the Mineral-Water and Particle-Water Interface in Natural Systems. New York,
NY: Wiley & Sons.
Taylor, J. C. (1971). “Structure of the alpha-form of uranyl hydoxide”. Acta Crystallogr., B27,
1088.
Taylor, J. C., and H. J. Hurst (1971). “The hydrogen atom locations in the α and β forms of
uranyl hydroxide”. Acta Crystallogr., B27, 2018–2022.
Taylor, J. C., J. W. Kelly and B. Downer (1972). “A Study of the β->α phase transition in
UO2(OH)2 by dilatometric, microcalorimetric and X-ray diffraction techniques”. Journal of Solid
State Chemistry, 5, 291–299.
Used Fuel Degradation: Experimental and Modeling Report October 2013 81
Thompson, A., and C. Wolverton (2011). “First-principles study of noble gas impurities and
defects in UO2”. Physical Review B, 84(13), 134111.
Weck, P., E. Kim, N. Balakrishnan, F. Poineau, C. Yeamans, and K. R. Czerwinski (2007).
“First-principles study of single-crystal uranium mono- and dinitride”. Chemical Physics Letters,
443(1-3), 82–86
Weck, P. F., E. Kim, C. F. Jové-Colón, and D. C. Sassani (2012). “Structures of uranyl peroxide
hydrates: a first-principles study of studtite and metastudtite”. Dalton Transactions, 41(32),
9748–9752.
Weck, P., C.-M. Gong, E. Kim, P. Thuery, and K. Czerwinski (2011). “One-dimensional
uranium-organic coordination polymers: crystal and electronic structures of uranyl-
diacetohydroxamate”. Dalton Transactions, 40(22), 6007–6011.
Weck, P., E. Kim, B. Masci, P. Thuery, and K. R. Czerwinski (2010). “Density Functional
Analysis of the Trigonal Uranyl Equatorial Coordination in Hexahomotrioxacalix[3]arene-based
Macrocyclic Complexes”. Inorganic Chemistry, 49(4), 1465–1470.
Wu, X., M. C. Vargas, S. Nayak, V. Lotrich, and G. Scoles (2001). “Towards extending the
applicability of density functional theory to weakly bound systems”. Journal of Chemical
Physics, 115, 8748.
Used Fuel Degradation: Experimental and Modeling Report 82 October 2013
14. SUMMARY AND CONCLUSIONS
The contributions presented in this report are being accomplished via a concerted effort among
three different national laboratories: SNL, ANL and PNNL. This collaborative approach
includes experimental work, process model development (including first-principles
approaches) and model integration—both internally among developed process models and
between developed process models and PA models. The main accomplishments of these
activities are summarized as follows:
Development of an idealized strategy for integrating used fuel degradation process
models with PA model approaches to analyze generic disposal environments includes
parametric connections/couplings needed for direct incorporation into PA models
(Section 1.2.2). However, it is an ongoing task to delineate in the implementation
specifics of how these process models will couple to other EBS process submodels
within the PA model for generic disposal environment evaluations of the safety case.
Additional more simplified coupling options are outlined that have fewer open
constraints on implementation specifics and provide flexible options for incorporating
additional coupling detail as needed.
Delineation of constraints for the instant release fraction (IRF –Section 1) from the
nuclear fuel implemented in two sets of distributions: (a) triangular distributions
representing minimum, maximum, and mean (apex) values for LWR UF with BU at or
below 50 MWd/KgU, and (b) uniform distributions as a function of BU representing
instantaneous radionuclide releases for UF with BU up to 75 MWd/KgU. In future
work, additional data may allow delineation of the accessible grain boundaries (and
pellet fractures) from inaccessible grain boundaries (and pellet fractures) to better
delineate constraints on the IRF. Currently, all grain boundaries (and pellet fractures)
are considered accessible.
Computational development and implementation of a radiolysis model (RM - Section
2) using a comprehensive set of coupled radiolysis kinetic reactions to better account
for potential solution compositions to be encountered in repository environments
(Wittman and Buck, 2012). Radiolytic species are generated at a rate that is based on
the dose rate induced by the used fuel radiation field deposited in the water film on the
fuel pellet. The current model covers the H2O system and allows for dissolved
carbonate by considering heterogeneous CO2 (aq) speciation including HCO-3.
Comparisons of modeling results are in good agreement with those reported in other
studies. The model inputs are the reaction rate constants, the temperature and dose rate,
the generation rates of radiolytic species, and the initial concentrations of species in the
system. In these idealized systems, hydrogen peroxide is the primary oxidizing species
generated in the radiolytic process. The conditional generation rate for H2O2 production
is the primary output provided to the model for matrix degradation rate (i.e., the mixed
potential model).
Computational implementation and verification/validation of the Canadian mixed
potential model for UO2 fuel corrosion in the initial mixed potential model (MPM -
Jerden et al., 2013). The objective of the MPM (Section 3) is to calculate the used fuel
degradation rates for a wide range of disposal environments to provide the source term
radionuclide release rates for generic repository concepts. The fuel degradation rate is
Used Fuel Degradation: Experimental and Modeling Report October 2013 83
calculated for chemical and oxidative dissolution mechanisms using mixed potential
theory to account for all relevant redox reactions at the fuel surface, including those
involving oxidants produced by solution radiolysis. This MPM is based on the
fundamental electrochemical and thermodynamic properties described by interactions
at the fuel – fluid interface and captures key processes such as hydrogen oxidation and
the catalysis of oxidation/reduction reactions by noble metal particles on the fuel
surface (epsilon phases). If radiolytic oxidants are exhausted by reaction with hydrogen
in the EBS (e.g., supplied from corrosion processes), then the degradation rate becomes
controlled by UO2 solubility constraints (chemical dissolution) and the degradation rate
is affected directly by the rate of transport of uranium away from the used fuel. If
oxidative dissolution is the dominant process, then the MPM directly calculates the rate
of used fuel matrix degradation.
Advanced strategies for coupling the RM and MPM into a single fuel matrix
degradation (FMD) module (Section 4) for use in analyzing the matrix degradation rate
(fractional and absolute) of used fuel (Section 4). Identification of parameters needed to
couple the codes together are given in detail, as well as are four strategies for
implementing the coupling of the two process models. Different options have
advantages and disadvantages based on the extent of coding that would be required and
the ease of use of the final product. The four approaches for implementing coupling are
o Option 1: Add radiolysis model as subroutine within mixed potential model
code.
o Option 2: Represent radiolysis model as an analytical expression within mixed
potential model code.
o Option 3: Provide radiolysis model results as look-up table of conditional
generation values produced by running the RM over the full range of relevant
conditions.
o Option 4: Maintain radiolysis model and mixed potential model as separate
codes that call each other during a fuel degradation model run.
The last of these four options is closest to the approach to the sensitivity analyses for
the MPM implemented within DAKOTA presented in Section 4.3.1. However,
integration of the RM into this implementation has not been completed at this point and
would require either a dynamic link library to implement, or additional coding within
the DAKOTA environment to manage parameter hand-offs between the MPM and RM.
A series of sensitivity analyses for the Mixed Potential Model (MPM) were conducted
by externally-coupling the MPM Matlab code with the DAKOTA toolkit in a Microsoft
Windows 7 environment. DAKOTA is an open source multilevel parallel object-
oriented framework developed at Sandia National Laboratories. The DAKOTA code
suite contains a large collection of algorithms to conduct optimization, uncertainty
quantification (UQ), and sensitivity analysis. The external coupling uses shell scripting
commands to post-process MPM output responses that are input to DAKOTA. The
MPM model inputs that were varied are temperature, dose rate, and initial carbonate
(CO3--) and oxygen (O2 (aq)) concentrations. This set of analyses contained 256 iteration
calculations. The output responses that were sampled are the concentrations UO2++
,
Used Fuel Degradation: Experimental and Modeling Report 84 October 2013
UCO3--, and H2O2. The UO2
++ and UCO3
—represent the total concentration of U
released into the system, hence reflect the degradation rate. In these initial sensitivity
analyses, the main influence in output U and H2O2 concentrations is the dose rate.
A computational first-principles study of the structures of the uranyl peroxide hydrates
studtite and metastudtite (Weck et al., 2012). The structures obtained from total energy
calculations using density functional theory are in very good agreement with those
characterized by experimental X-ray diffraction methods. Such work tests this
computational tool to predict the phase stability of UO2 corrosion products and quantify
their thermodynamic properties for use with similar studies of UO2 bulk and surface
chemistry (Weck et al., 2013).
14.1 Concluding Remarks and Future Development
Our general strategy for integrating process models with each other, and within the
performance assessment models, is to identify initially the major feeds among the process
models (Section 4) and from the process models to performance assessment models (Section
1). For coupling into performance assessment models, our approach begins by using the
existing interface connections in the PA model and progresses to adding further connections as
the process models develop and become more highly coupled. The ultimate objective is to
support the PA models with a single coupled process model for analyzing the fractional
degradation rate of used fuel. Note that even after coupling, the radiolysis model (RM) and the
mixed potential model (MPM) can still be used individually for detailed sensitivity and
uncertainty analyses as well.
Currently, the MPM has been coupled with DAKOTA to perform parametric sensitivity analyses
for major input variables such as radiation flux, temperature, and chemical species variability.
The DAKOTA code provides one possible means of handshaking or coupling the MPM with the
RM. Within any coupling implementation, identifying the essential parameters to be exchanged
is the primary step. One of these is the conditional generation rate of hydrogen peroxide (Gcond)
as a function of energy deposition in the water film on the used fuel pellet surface. The value of
Gcond is calculated in the RM and handed off to the MPM. Within the MPM, the Gcond is used to
calculate the spatial generation of [H2O2] from the dose rate as affected by surface reactions with
the fuel and diffusive flux of the species.
The coupling of the RM and MPM is implemented currently by running the models separately
because the MPM uses time steps on the order of years, whereas the RM uses time steps on the
order of seconds. An alternative to actively linking the RM and MPM (perhaps within
DAKOTA) is to develop an analytic expression that determines Gcond for a given set of
conditions. The analytic expression could be coded directly into the MPM via the MATLAB
implementation, and thus run directly within the MPM. However, this simplification does not
establish a true working link and the full capabilities of RM would be lost without further work.
Furthermore, the determination of analytical expressions for the full ranges of environments may
prove to be onerous.
Currently the only radiolytic species in the MPM is H2O2. Other radiolytic species will need to
be added to the MPM for it to be applicable to the full range of relevant geologic and EBS
environments. The radiolytic species that need to be added can be determined by sensitivity runs
using the RM (which evaluates a more detailed set of compositional components) for the range
Used Fuel Degradation: Experimental and Modeling Report October 2013 85
of relevant solution compositions for sites of interest. The focus of RM sensitivity runs is on
radiolytically active species (for example: Cl-, Br
-, NO3
-, CO3
2-, SO4
2-) and can be used to
determine concentration thresholds above which radiolytic species other than H2O2 significantly
impact fuel oxidation.
Density functional theory (DFT) calculations of the thermodynamic properties of crystalline
studtite, (UO2)O2(H2O)4, and metastudtite, (UO2)O2(H2O)2, were carried out within the generalized
gradient approximation to derive both their isochoric and isobaric thermal properties. Further
experimental work is needed to assess our theoretical predictions for these SNF corrosion phases.
This methodology will be applied in a systematic way to other possible metastable corrosion
phases and other NS and EBS models to expand the applicability of this data set to more realistic
systems. In addition, polymorphism in stoichiometric dehydrated schoepite, UO2(OH)2, was
investigated using computational approaches that go beyond standard DFT. The results show that
standard DFT is sufficient for this system. The three UO2(OH)2 phase structures optimized with
standard DFT will be used in future calculations of the thermodynamic stability and phase
transitions in this compound.
For the UFD&RM process models and/or coupled modules, the primary connection into the
performance assessment models is the fractional degradation rate (FDR) parameter, which is
currently sampled from a distribution. This primary connection has been the focus for developing
more process-based models that are able to supplant the FDR distribution by supplying that
parameter directly as a result of the process model. In addition, a second connection within the
PA model could be generated to represent the instant release fractions. Sampling of the IRF
distributions within the PA model would be done similar to the current sampling of the FDR
distribution and would describe the fast/instant release fraction radionuclides that are mobilized
instantly at the time of cladding breach. The distributions for the IRF would only need to be
sampled at the initiation of UF degradation for each fuel rod represented as having a breach in its
cladding.
Used Fuel Degradation: Experimental and Modeling Report 86 October 2013
15. APPENDICES
Used Fuel Degradation: Experimental and Modeling Report October 2013 87
Appendix 1
MATLAB Code for NMP Catalysis Domain Reactions
The MATLAB code for implementation of the MPM is divided into six files that must be open
within the MATLAB operation folder to run the MPM. The MPM files are:
AMP.m is a data container that holds information on simulation time steps, grid spacing,
temperature, dose rate, H2O2 generation, species stoichiometry, saturation concentrations,
diffusion coefficients, porosity, tortuosity of corrosion layer etc.
AMP_reactSurf.m defines all surface reactions and calculates the rates of surface
processes (reaction currents) and the fuel corrosion potential. This file contains all
information needed for calculating rates of all surface redox reactions and is thus the
heart of the MPM. It is called recursively when throughout a simulation.
AMP_reactBulk.m defines reactions and calculates the rates of processes that occur in the
space between the fuel surface and the environmental boundary at the end of the model
diffusion grid (right hand boundary in Figure 6).
AMP_main.m is a top level function that calls all the other files needed to run the MPM.
AMP_error.m provides the status function, matrix calculations and input arguments for
the MATLAB ordinary differential equation solver.
AMP_output.m writes simulation results as space delimited text files.
The sections of code that were added to the existing MATLAB MPM to implement the NMP
catalyst domain reactions are shown below. Black text is active code and green text are
comments.
The following was added to the AMP.m file to allow the modeler to set the resistance between
the NMP domain and the fuel matrix and to set the fractional surface coverage of NMP:
% Noble Metal Particle Domain Properties
function props = NMP_prop()
% Effective resistance between fuel and NMP domains
props.resist = 1.0e-3; % V/A (NOT ZERO; choose something small)
% Fraction surface coverage of noble metal particles
props.frac = 0.01; % fraction
Used Fuel Degradation: Experimental and Modeling Report 88 October 2013
The following was added to the AMP_reactSurf file. These lines define new surface redox
reactions and calculate reaction currents and the corrosion potential of the NMP domain.
%**************************************************************************
function [rMat,dMat,oFun,dFun,eCorr,cDen] = AMP_reactSurf(T,conc,eCrG,oFlg)
% Initialize parameters
[nCmps,~] = size(conc);
iSS = (AMP.valD(298)>0);
nSS = sum(iSS);
% Initialize current density data container
cDen = cell(0);
% Initialize missing arguments
if(nargin<4)
oFlg = false;
end
if(nargin<3)
eCrG = 0;
end
% Retrieve simulation values
F = AMP.constF();
R = AMP.constR();
datNMP = AMP.NMP_prop();
% Calculate temperature dependence factor
dT = (1/298-1/T)/R;
%**********************************%
% Fuel Surface Reactions %
%**********************************%
% Initialize domain objectives
oFun = zeros(2,1);
Used Fuel Degradation: Experimental and Modeling Report October 2013 89
% Initialize reaction rates and derivatives
rMat = zeros(nCmps,1);
dMat = zeros(nSS,nSS);
% Initialize derivative accumulators
dRdE1 = zeros(nSS,1); dE1dcT1 = zeros(1,nSS); dE1dcT2 = 1;
dRdE2 = zeros(nSS,1); dE2dcT1 = zeros(1,nSS); dE2dcT2 = 1;
% Validate corrosion potentials
if(length(eCrG)<length(oFun))
eCorr = zeros(length(oFun),1);
else
eCorr = eCrG;
end
% Calculate corrosion potential (recursive)
if(~oFlg)
[~,~,oFun,dFun] = AMP_reactSurf(T,conc,eCorr,true);
dEcorr = dFun\oFun;
while(max(abs(oFun)) > 1e-20 && max(abs(dEcorr)) > 1e-15)
eCorrNew = eCorr - dEcorr;
[~,~,oFunT,dFun] = AMP_reactSurf(T,conc,eCorrNew,true);
if(sum(oFunT.^2) < sum(oFun.^2))
eCorr = eCorrNew; oFun = oFunT;
dEcorr = dFun\oFun;
else
dEcorr = dEcorr/2;
end
end
end
% Domain potentials
eFuel = eCorr(1);
eNMP = eCorr(2);
% Domain surface fractions
Used Fuel Degradation: Experimental and Modeling Report 90 October 2013
fFrac = 1-datNMP.frac;
pFrac = datNMP.frac;
% Voltage difference contribution
oFun(:) = eNMP-eFuel;
dFun = [-1, 1;-1, 1];
%**********************************%
% Start NMP Domain Reactions %
%**********************************%
% Required specifications for each surface reaction
% kVal: reaction rate constant (mol/m^2/s; or appropriate)
% eNum: number of electrons generated
% ECTC: electrochemical charge transfer coefficient
% Ezro: standard potential (Vsce)
% sMat: stoichiometry of reaction
% oMat: reaction order in concentrations
%**********************************%
% NMP 1: Reaction 7 %
% H2O2 + 2e(-) -> 2OH(-) %
%**********************************%
% Initialize vectors
oMat = zeros(nCmps,1);
sMat = zeros(nCmps,1);
% Values unique to reaction
kVal = 1.2e-11*exp(6.0e4*dT); %Place holder - vary
eNum = -2;
ECTC = -0.4; %Place holder - same as UO2
eZro = 0.973-0.000698*(T-298); %Place holder - same as UO2
sMat(AMP.H2O2) = -1;
oMat(AMP.H2O2) = 1;
Used Fuel Degradation: Experimental and Modeling Report October 2013 91
% Reaction rate
rRat = pFrac*kVal*exp(ECTC*F/R/T.*(eNMP-eZro))*prod(conc.^oMat);
% Corrosion potential objective functions, derivatives
if(oFlg)
oFun(2) = oFun(2) - 2*datNMP.resist*F*eNum*rRat;
dFun(2,2) = dFun(2,2) - 2*datNMP.resist*F*eNum*rRat*ECTC*F/R/T;
end
% Current density
cDen = [cDen,{F*eNum*rRat}];
% Reaction rates and derivatives
if(~oFlg)
rMat = rMat + sMat*rRat;
dRdc = rRat*(oMat(iSS)./conc(iSS))';
dRdE2 = dRdE2 + rRat*(ECTC*F/R/T)*sMat(iSS);
dE1dcT1 = dE1dcT1 - 2*datNMP.resist*F*eNum*dRdc;
dE1dcT2 = dE1dcT2 - 2*datNMP.resist*F*eNum*rRat*(ECTC*F/R/T);
dMat = dMat + sMat(iSS)*dRdc;
end
%**********************************%
% NMP 2: Reaction 8 %
% (1/2)H2 + OH(-) -> H2O + e(-) %
%**********************************%
% Initialize vectors
oMat = zeros(nCmps,1);
sMat = zeros(nCmps,1);
% Values unique to reaction
kVal = 1.0*exp(6.0e4*dT);
eNum = 1;
ECTC = 0.4;
eZro = 0.9-0.001900*(T-298);
Used Fuel Degradation: Experimental and Modeling Report 92 October 2013
sMat(AMP.H2) = -0.5;
oMat(AMP.H2) = 1;
% Reaction rate
rRat = pFrac*kVal*exp(ECTC*F/R/T.*(eNMP-eZro))*prod(conc.^oMat);
% Corrosion potential objective functions, derivatives
if(oFlg)
oFun(2) = oFun(2) - 2*datNMP.resist*F*eNum*rRat;
dFun(2,2) = dFun(2,2) - 2*datNMP.resist*F*eNum*rRat*ECTC*F/R/T;
end
% Current density
cDen = [cDen,{F*eNum*rRat}];
% Reaction rates and derivatives
if(~oFlg)
rMat = rMat + sMat*rRat;
dRdc = rRat*(oMat(iSS)./conc(iSS))';
dRdE2 = dRdE2 + rRat*(ECTC*F/R/T)*sMat(iSS);
dE1dcT1 = dE1dcT1 - 2*datNMP.resist*F*eNum*dRdc;
dE1dcT2 = dE1dcT2 - 2*datNMP.resist*F*eNum*rRat*(ECTC*F/R/T);
dMat = dMat + sMat(iSS)*dRdc;
end
%**********************************%
% End NMP Reactions %
%**********************************%
% Derivative cleanup
if(~oFlg)
dE1dc = (dE1dcT1 + dE1dcT2*dE2dcT1)/(1-dE1dcT2*dE2dcT2);
dE2dc = (dE2dcT1 + dE2dcT2*dE1dcT1)/(1-dE2dcT2*dE1dcT2);
dMat = dMat + dRdE1*dE1dc;
dMat = dMat + dRdE2*dE2dc;
Used Fuel Degradation: Experimental and Modeling Report October 2013 93
end
%**********************************%
% End Fuel Surface Reactions %
%**********************************%
return
%**************************************************************************
Definitions of MATLAB commands used in code:
classdef: begins the class definition. There are many different data types, or classes, in MATLAB. You can build matrices and arrays of floating-point and integer data, characters and strings, and logical true and false states.
static methods are associated with a class, but not with specific instances of that class. These methods do not perform operations on individual objects of a class and, therefore, do not require an instance of the class as an input argument, like ordinary methods. Static methods are useful when you do not want to first create an instance of the class before executing some code. For example, you might want to set up the MATLAB environment or use the static method to calculate data needed to create class instances.
Rvec: vector of reaction rates.
sMat: stoichiometry matrix.
oFun: objective function.
dFun: derivative function.
Ecorr: corrosion potential (Vsce)
nargin<4 returns the number of input arguments passed in the call to the currently executing function.
abs(X) returns an array Y such that each element of Y is the absolute value of the corresponding element of X.
C = min(A) returns the smallest elements along different dimensions of an array.
The odeset function lets the user adjust the integration parameters of the relevant ordinary differential equation solvers.
[tvec,Xout] = ode15s(@MPM_odefun, [0.01 tmax], X0,opts,params) integrates the system of differential equations y′ = f(t,y) from time t0 to tf with initial conditions y0. Default integration parameters are replaced by property values specified in options, an argument created with the odeset function. The MATLAB ode15s solver is preferred for stiff problem types.
odefun: A MATLAB function handle that evaluates the right side of the differential equations. Provides input arguments to MATLAB ordinary differential equation solvers.
TF = isempty(A) returns logical 1 (true) if A is an empty array and logical 0 (false) otherwise. An empty array has at least one dimension of size zero.
X = reshape(A,m,n) returns the m-by-n matrix B whose elements are taken column-wise from A. An error results if A does not have m*n elements.
Used Fuel Degradation: Experimental and Modeling Report 94 October 2013
Appendix 2
Electrochemical Experiment Results
The results of electrochemical experiments are documented in EXCEL files in the DOE FCRD
Document Management System as supporting data for the report FCRD-UFD-2013-000305.
Separate files are provided for analyses conducted as a group, in most cases on the same day.
The following tables summarize the electrodes and electrolytes that were used in the experiments
and the analyses documented in file. Experiments were conducted using UO2 ceramic without
dopants and a representative NMP material made with Re as a surrogate for Tc referred to as
NMP-W. Most experiments were conducted in electrolytes containing 1 mM NaCl that had been
adjusted to a final pH of 9.5 by the addition of a dilute NaOH solution (about 1 mM NaOH); a
few electrolytes were adjusted to acidic pH values using H2SO4. Many experiments were
conducted in electrolytes with various amounts of added H2O2. Experiments were conducted
with the as-prepared electrolytes exposed to air, or purged with argon gas or a mixture of about
3% hydrogen in helium gas referred to as regen gas.
Electrochemical analyses (Tables 2.1 through 2.7 of this appendix) included potentiodynamic
(PD) sweeps, Tafel scans, linear polarization resistance (LPR) scans, electrochemical impedance
spectroscopy (EIS), and cyclic voltammetry (CV) analyses. The actual data files are in
VersaStudio format collected by Princeton Applied Research software and are being maintained
at ANL for continued analyses. Complete results for key analyses with UO2 and NMP alloy W
are included as listed in Table 2.7 and include potentiostatic (PS) and open circuit corrosion
(OC) results). Results for the individual analyses have been copied to EXCEL worksheets for
convenience in storage and future use. Several experiments were commonly conducted
sequentially on the same day and those data are compiled in the same EXCEL workbook. Each
workbook contains a worksheet with the protocol for the suite of electrochemical experiments
and information regarding the electrode and electrolyte.
Used Fuel Degradation: Experimental and Modeling Report October 2013 95
Table 2.1 EXCEL files for experimental results with UO2 electrodes in air
Folder and EXCEL Workbook File Name Electrolyte Analyses in File
UO2/Air/Sample 1 NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2 1 1mM NaCl AirJuly 26 2012 1E-3 M — — — yes yes yes yes no
UO2 1 1mM NaCl NaOH pH 9.5 1E-4M H2O2 AirAug 15 2012 1E-3 M pH 9.5 1E-4 M — yes no no yes no
UO2 1 NaOH pH 9.5 1E-2M H2O2 AirJuly 25 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
UO2 1 NaOH pH 9.5 1E-4M H2O2 AirJuly 21 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
UO2 1 NaOH pH 9.5 1E-6M H2O2 AirJuly 18 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
UO2 1 NaOH pH 9.5 1E-8M H2O2 AirJuly 19 2012 1E-3 M pH 9.5 1E-8 M — yes yes yes yes no
UO2 1 NaOH pH 9.5 Air Oct 17 2012 1E-3 M pH 9.5 — — yes yes yes yes no
UO2 1 NaOH pH 9.5 AirJuly 16 2012 1E-3 M pH 9.5 — — yes yes yes yes no
UO2/Air/Sample 1/CV
UO2 1 1mM H2O2 Air Oct 17 2012 — — 1E-3 M — no no no yes yes
UO2 1 1mM NaCl Air Oct 9 2012 1E-3 M — — — no no no yes yes
UO2 1 1mM NaCl Air Oct 18 2012 1E-3 M — — — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 23 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 19 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 Air Oct 10 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 Air Oct 18 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 1 NaOH pH 9.5 Air Oct 17 2012 — pH 9.5 — — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report 96 October 2013
UO2/Air//Sample 2/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2 2 1mM H2O2 Air Oct 17 2012 — — 1E-2 M — no no no yes yes
UO2 2 1mM NaCl Air Oct 18 2012 1E-3 M — — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 19 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 Air Oct 10 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 2 1mM NaCl NaOH pH 9.5 Air Oct 18 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 2 NaOH pH 9.5 Air Oct 17 2012 — pH 9.5 — no no no yes yes
UO2/Air/Sample 3/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2 3 NaOH pH 9.5 Air Oct 17 2012 — pH 9.5 — no no no yes yes
UO2 3 1mM H2O2 Air Oct 17 2012 — — 1E-3 M — no no no yes yes
UO2 3 1mM NaCl Air Oct 18 2012 1E-3 M — — — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 19 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 Air Oct 10 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 3 1mM NaCl NaOH pH 9.5 Air Oct 18 2012 1E-3 M pH 9.5 — — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report October 2013 97
Table 2.2 EXCEL files for experimental results with UO2 electrodes in electrolyte purged with argon gas
UO2/Argon NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2 1 1mM NaCl Argon July 31 2012 1E-3 M — — — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-2M H2O2 Argon June 28 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-4M H2O2 Argon July 11 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-6M H2O2 Argon June 26 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-8M H2O2 Argon July 25 2012 1E-3 M pH 9.5 1E-8 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 Argon July 13 2012 1E-3 M pH 9.5 — — yes yes yes yes no
UO2/Argon/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2 1 1mM H2O2 Argon Oct 25 2012 — — 1E-3 M — no no no yes yes
UO2 1 1mM NaCl Argon Oct 23 2012 1E-3 M — — — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Argon Oct 30 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Argon Oct 29 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Argon Oct 29 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Argon Oct 25 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2 1 1mM NaCl NaOH pH 9.5 Argon Oct 24 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2 1 NaOH pH 9.5 Argon Oct 24 2012 — pH 9.5 — — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report 98 October 2013
Table 2.3 EXCEL files for experimental results with UO2 electrodes in electrolyte purged with regen gas
UO2/Regen NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2#1 1mM NaCl Regen July 27 2012 1E-3 M — — — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-2M H2O2 Regen July 12 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-4M H2O2 Regen July 5 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-6M H2O2 Regen July 2 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 1E-8M H2O2 Regen July 20 2012 1E-3 M pH 9.5 1E-8 M — yes yes yes yes no
UO2#1 NaOH pH 9.5 Regen July 17 2012 1E-3 M pH 9.5 — — yes yes yes yes no
UO2/Regen/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
UO2# NaOH pH 9.5 Regen Nov 1 2012 — pH 9.5 — — no no no yes yes
UO2#1 1mM H2O2 Regen Nov 5 2012 — — 1E-3 M — no no no yes yes
UO2#1 1mM NaCl NaOH pH 9.5 Regen Nov 2 2012 1E-3 M pH 9.5 — — no no no yes yes
UO2#1 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen Nov 9 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
UO2#1 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Regen Nov 8 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
UO2#1 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Regen Nov 7 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
UO2#1 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Regen Nov 6 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
UO2#1 1mM NaCl Regen Oct 31 2012 1E-3 M — — — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report October 2013 99
Table 2.4 EXCEL files for experimental results with NMP-W electrode in air
NMPW Alloy/Air NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
NMP-W 1mM H2O2 Air Mar 16 2012 — — 1E-3 M — yes yes yes yes no
NMP-W 1mM NaCl 0.025M H2SO4 Air May 14 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl Air Apr 22 2012 1E-3 M — — — yes yes yes yes no
NMP-W 1mM NaCl Air July 17 2012 1E-3 M — — — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air July 26 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air May 4 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air May 18 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Air July 20 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Air May 2 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 H2SO4 pH 3 Air May 9 2012 1E-3 M pH 9.5 1E-4 M 1E-4 M yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Apr 25 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air July 19 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air July 27 2012 1E-3 M pH 9.5 1E-8 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 Air Apr 24 2012 1E-3 M pH 9.5 — — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5Air July 18 2012 1E-3 M pH 9.5 — — yes yes yes yes no
NMPW Alloy/Air/CV
NMP-W 1mM H2O2 Air May 16 2012 — — 1E-3 M — no no no yes yes
NMP-W 1mM NaCl Air April 17 2012 1E-3 M — — — no no no yes yes
NMP-W 1mM NaCl Air Oct 18 2012 1E-3 M — — — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 then H2SO4 pH 3 Air May 11 2012
1E-3 M pH 9.5 1E-4 M 1E-4 M no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report 100 October 2013
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 11 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Air Oct 23 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Air Oct 19 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 Air Oct 18 2012 1E-3 M pH 9.5 — — no no no yes yes
NMP-W NaOH pH 9.5 1E-2M H2O2 Air May 18 2012 — pH 9.5 1E-2 M — no no no yes yes
NMP-W NaOH pH 9.5 Air Oct 17 2012 — pH 9.5 — — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Air Oct 12 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
NMP-W 1mM H2O2 0.025M H2SO4 Air May 14 2012 — — 1E-3 M 2.5E-2 M no no no yes yes
Table 2.5 EXCEL files for experimental results with NMP-W electrode in electrolyte purged with argon gas
NMPW Alloy/Argon/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
NMP-W 1mM H2O2 Argon Oct 25 2012 1E-3 M — — — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 Argon Oct 24 2012 — pH 9.5 1E-2 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Argon Oct 30 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Argon Oct 29 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Argon Oct 29 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Argon Oct 25 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report October 2013 101
Table 2.6 EXCEL files for experimental results with NMP-W electrode in electrolyte purged with regen gas
NMPW Alloy/Regen NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
NMP-W 0.025M H2SO4 1mM H2O2 Regen Mar 15 2012 1E-3 M — — 2.5E-2 M yes yes yes yes no
NMP-W 1mM H2O2 Regen Mar 17 2012 — — 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Regen Aug 1 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Regen Aug 3 2012 1E-3 M pH 9.5 1E-8 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5l Regen Apr 2 2012 1E-3 M pH 9.5 — — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen Aug 6 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen May 7 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen May 20 2012 1E-3 M pH 9.5 1E-2 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Regen Aug 2 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Regen May 3 2012 1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2H2SO4 pH 3 Regen May 10 2012
1E-3 M pH 9.5 1E-4 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Regen Apr 30 2012 1E-3 M pH 9.5 1E-6 M — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 Regen July 25 2012 1E-3 M pH 9.5 — — yes yes yes yes no
NMP-W 1mM NaCl NaOH pH 9.5 Regen Mar16 2012 1E-3 M pH 9.5 — — yes yes yes yes no
NMP-W 1mM NaCl Regen Apr 23 2012 1E-3 M — — — yes yes yes yes no
NMP-W 1mM NaCl Regen July 31 2012 1E-3 M — — — yes yes yes yes no
NMPW Alloy/Regen/CV NaCl NaOH H2O2 H2SO4 LPR Tafel PD EIS CV
NMP-W 1mM H2O2 Regen Nov 5 2012 — — 1E-3 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen Nov 9 2012 — pH 9.5 1E-2 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-4M H2O2 Regen Nov 8 2012 1E-3 M pH 9.5 1E-4 M — no no no yes yes
Used Fuel Degradation: Experimental and Modeling Report 102 October 2013
NMP-W 1mM NaCl NaOH pH 9.5 1E-6M H2O2 Regen Nov 7 2012 1E-3 M pH 9.5 1E-6 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 1E-8M H2O2 Regen Nov 6 2012 1E-3 M pH 9.5 1E-8 M — no no no yes yes
NMP-W 1mM NaCl NaOH pH 9.5 Regen Nov 2 2012 1E-3 M pH 9.5 — — no no no yes yes
NMP-W Alloy 0.025M H2SO4 1mM H2O2 Regen May 15 2012 — — 1E-3 M — no no no yes yes
NMP-W Alloy 1mM H2O2 Regen May 16 2012 — — 1E-3 M — no no no yes yes
NMP-W Alloy 1mM NaCl Regen Apr 17 2012 1E-3 M — — no no no yes yes
NMP-W Alloy 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen Apr 6 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
NMP-W Alloy 1mM NaCl NaOH pH 9.5 1E-2M H2O2 Regen May 22 2012 1E-3 M pH 9.5 1E-2 M — no no no yes yes
NMP-W Alloy 1mM NaCl NaOH pH 9.5 H2SO4 pH3 1E-4M H2O2 Regen May 11 2012
1E-3 M pH 9.5 1E-4 M 1E-3 M no no no yes yes
NMP-W Alloy 1mM NaCl NaOH pH 9.5 Regen Apr 18 2012 1E-3 M pH 9.5 — — no no no yes yes
Table 2.7 EXCEL files with collection data
UO2/UO2 VersaStudio NaCl NaOH H2O2 OC LPR Tafel PD PS EIS
PS UO2 E-2 1E-3 M pH 9.5 1E-2 M yes no no no yes yes
UO2 H2O2 1E-3 M pH 9.5 various yes yes yes yes yes yes
UO2 NaCl NaOH 1E-3 M pH 9.5 No yes yes yes yes yes yes
W H2O2 1E-3 M pH 9.5 various yes yes yes yes yes yes
W NaCl NaOH 1E-3 M pH 9.5 No yes yes yes yes yes yes
Used Fuel Degradation: Experimental and Modeling Report September 2013 103